boomerang 155, 156 Borel-Pompeiu's formula 327 bosonic and fermioni c fields 202 INDEX Bourbaki, N. 113, 117 braid group 400, 402 A. braid operator 400 algebra, 'Zl2 graded 29, 34, 281, 284 braided correlation 399 algebra, central 117 braided deform ation 391 algebra, deformation of xi, 397 braided monoid al category 399 algebra, faithfu l repr esentations of 282 braiding ru les 391 algebra, indecomposable ideals in 121 Burnside's Theorem 71 algebra, left regular representation of 283 algebra, minimal left ideal of 282 C. algebra, nilpotent ideals in 122 Caley-Klein parameters 4 algebra, quantization of 397 caps on quadrics 59 algebra, quotient 29, 30, 34 Cartan's tri ality principle 37, 140 algebra, radical of 121 Cartan, Elie 8, 117, 149, 205, 206, 372, 384 Casimir operator 23 algebra, semi-simple 121 n algebra, simple 76, 117, 283 Cauchy's integral form in lC 302 algebra, symmetric 29 Cayley numb ers 37 algebra, universal enveloping 33 Cayley, Arthur 4, 5, 10 Alhfors, L.V. 301 Cayley-Dickson pro cess 48 aljabr 3 Cayley-Hamilton th eorem 101, 105 anticommuting set (AS) 70 Cayley-Klein parameters 4 axial vectors 5 centralizing pairs 79 charge conjugation 9, 26 B. Chevalley's construction 137, 138 bilinear covariants 137, 149, 154, 157 Chevalley, Claude ix, 9, 10, 113, 117, 125, 137, bilinear form , alt ernating 59, 60, 62, 63, 65, 138,140,144,206,214,405,406 68,114,144 Chevalley-Kiihler deformation 406 bilinear form , antisymm etric 114 c1iffor 321 bilinear form, in characteristic 2 114 cliffor , Pauli 318 bilinear form, reflexive 114 cliffor, real 314 bilinear form, symmetric 114 cliffor-valued functions 313 biquat ernion 7, 26, 266 Clifford algebra Gi 3•1 281, 286 biquaternion algebra 314 Clifford algebra Gi 3,1 , graded left regular rep­ biquat ernion, complex 313 resentation of 286 biquaternion, conjugation of 266, 269, 313 Clifford algebra Gi3 ,1 , main automorphisms biquat ernion, norm of 266 of 292 biquaternion, real 265, 313 Clifford algebra Gin outermorphisms 106 biquaternion, real, regular functions of 265, Clifford algebra 59, 157, 325, 348, 358 269, 270 Clifford algebra and Dirac equation 149 bivector 7, 127, 139, 148, 313 Clifford algebra as a twisted tensor product 35 bivector, in characteristic 2 147 Clifford algebra bundle, hyperbolic 177, 196 bivector, simple 148, 162 Clifford algebra for Heeke braid 409 bivectors, generating Spio+(1,3) 179 Clifford algebra ideals, algebraic equivalence

413 414 of 180 Clifford algebra, real 3, 6, 15, 25, 26, 27, 33, Clifford algebra ideals, geometric equivalence 34,59,76,101,149,382 of 180, 184, 185 Clifford algebra, reduced left regular represen­ Clifford algebra structure, generalizations of tations of 129 383 Clifford algebra, Riesz's exterior product in Clifford algebra, Cit ,3 25, 180 147 Clifford algebra, Cit ,3 , complexified 150, 163, Clifford algebra, structure of 35, 117 188 Clifford algebra, symplectic ix, x, xi, 410 Clifford algebra, Ci3 24, 126, 127, 130, 313 Clifford algebra, two valued representation of Clifford algebra, Ci4 ,l 181, 188 9 Clifford algebra, 7l2-gradationof72, 138, 141, Clifford algebra, universal x, 59 147 Clifford algebras and algebraic spinors 117 Clifford algebra, as a Chevalley-Kahler defor­ Clifford algebras and binary codes 87 mation of a quadratic algebra 406 Clifford algebras and design theory 87 Clifford algebra, as a deformation of exterior Clifford algebras and electrodynamics 265 algebra x, 398 Clifford algebras and graph theory 87 Clifford algebra, as a subalgebra of an endo­ Clifford algebras and spinor ideals 117, 119 morphism algebra 137, 144 Clifford algebras as matrix algebras 140 Clifford algebra, as extensive quantity 6 Clifford algebras , characteristic 2 50, 52 Clifford algebra, commutative 49 Clifford algebras , extrinsic view of 105 Clifford algebra, complexification of 71, 72, Clifford algebras, intrinsic view of 106 126,150,163,281,335,352 Clifford algebras, isomorphic to matrix alge­ Clifford algebra, definition of ix, x, 137 bras 35,281 Clifford algebra, degenerate 114 Clifford algebras, periodicity of x, 35, 140 Clifford algebra, derivations in 106, 142, 148 Clifford algebras, spinor representations of 288 Clifford algebra, dimension grading in 72, 107, Clifford algebras, spinor structure of 106 137, 141, 148 Clifford algebras, table of 61, 71, 72 Clifford algebra, even subalgebra of 7, 167 Clifford bundle 120, 375 Clifford algebra, finite 9 Clifford bundle of space-time 186 Clifford algebra, graded opposite algebra of Clifford bundle of space-time, bundle of ideals 138 187 Clifford algebra, hermitian conjugation in 127 Clifford bundle of space-time, irreducible Clifford algebra, hyperbolic 193 module representations of 186, 189 Clifford algebra, in characteristic 250, 52, 145 Clifford bundle of space-time, spinor bundles Clifford algebra, isomorphism with exterior al­ 187, 188 gebra as left modules 141 Clifford bundle on SD-l with spin structure Clifford algebra, minimal left (right) ideals of 199 178,281 Clifford bundle, hyperbolic 197 Clifford algebra, nilpotent r-vectors in 113 Clifford conjugation 127,313, 314, 316 Clifford algebra, of Hardy- Weiberg quadratic Clifford group 36, 117, 203 form 55 Clifford group and pin group 117 Clifford algebra, of projective modules of finite Clifford group and spin group 117 type xi Clifford map 144, 197,405 Clifford algebra, principal ideals in 113 Clifford module 9 Clifford algebra, pseudovector in 7 Clifford norm 36 Clifford algebra, quantum braided 387, 392 Clifford numbers 172, 177, 345 415

Clifford product z, 6, 8, 139, 142, 148 diffraction of light, by a square hole 280 Clifford spin bundle 190, 192 Dirac d-number 25 Clifford's geometric algebra 125, 133 Dirac algebra 36, 160, 180 Clifford, William Kingdon 6, 7, 24 Dirac conjugation 120, 151 Clifford-Lipschitz group, definition 179 Dirac equation 26, 137, 149, 158, 174 Clifford-Pompeiu formula 302, 307 Dirac equation, a multivector form of 159 compact Kahler spin manifold 246 Dirac equation, in spinor form 289 complete boundary collocation system 335 Dirac equation, massive 297 cone integrals 307 Dirac equation, massless 281, 282, 290, 295 cones, elliptic and hyperbolic 65, 88 Dirac equations, Lagrangians for 292 conformal group 305 Dirac gamma matrices 149, 182 conformal symmetry 24 Dirac group, automorphisms of 59, 85 conformal transformations 159 Dirac group, center of 74 contraction 137, 139 Dirac group, central extension of 59, 70, 81 contraction on a spinor space 214 Dirac group, definition of 59, 60 contraction, as a derivation 148 Dirac group, even 73 contraction, left/right 142 Dirac group, finite 59, 61 Conwell's heptad 59, 83, 89, 97 Dirac group, Frobenius-Schur indicator of 71 correlation on a vector space 139 Dirac group, normal subgroups of 79 Crowe, M.J. 3 Dirac group, of hyperbolic type 80 Crumeryolle's spinoriality transformations Dirac matrices 8, 172, 296 137, 149, 163 Dirac operator 243, 244, 249, 257, 301, 366 Crumeyrolle's "real" Witt basis 117 Dirac propagator 199, 200, 201 Crumeyrolle's amorphic spinor fields 177, 192 Dirac quantum field 257 Crumeyrolle's bivector xi, 137 Dirac quantum field, invariance under charge Crumeyrolle's spinor 137, 163 conjugation 260 Crumeyrolle's spinoriality group 163 Dirac quantum field, parity invariance of 261 Crumeyrolle, Albert ix-xiv, 3, 9, 15, 24, 41, Dirac quantum field, time reversal invariance 81,108,113,114, 116,117,119,120,121, 125, of 262 134, 135, 137, 138, 163, 177, 192, 196, 199, Dirac quantum field, translational invariance 200, 206, 214, 238, 257, 281, 282, 288, 291, of 260 296,301,365,377,387,402,407 Dirac self-adjoint multivector 156 Crumeyrolle-Chevalley spinors 125, 199, 203 Dirac spinor 15, 24, 133, 149, 167, 184, 185, Cuntz algebra 376 188, 258, 284, 291 curvature tensor 186 Dirac spinor fields 178, 185, 188, 190, 191,281 curved spacetimes 128 Dirac spinor, charge conjugation of 151 Dirac spinors and Clifford algebra Cl l ,3 172, D. 173,180,258 d'Alembertian operator 269 Dirac spinors as one-column spinor matrices de Montessus' theorem 352 239 decomposition of the unity 113 Dirac spinors without Clifford algebra 169 degenerate quadratic space 113 Dirac's current vector 138, 163 differential forms 178, 191, 197, 379 Dirac-Hestenes equation 167, 175 diffraction of light 265 Dirac-Kahler fields 193 diffraction of light, by a circular hole 279 Dirac-Kahler spinors 177 diffraction of light, by a narrow slit 278 directed random walk 199 416 domain manifold 338, 340 Domb-Joyce model 203 G. dual two-component spinors 168 Geroch 's theorem 192 dyadics 5 Gibbs, Josiah Willard 5 grad ed algebras 28 E. grad ed algebras, canonical structure of 28 Einstein space, non-compact , of negative grad ed algebras, morphisms 28 scalar curvature 251 grad ed algebras, tensor products of 28 electromagnetic field 26, 290 graded tensor product space 382 electromagnetic moment bivector 138, 163 graded vector space 28 elliptic boundary value probl em 325 grad ed-differential *-algebra 369 endomorphism algebra 101,107 Grassmann algebra 30, 106,121,211,216,379 enveloping algebra 71 Grassmann algebra, quantized 389 Euler angles 10, 22 Grassmann algebra, quantum braid ed 392 Euler-Lagrange equations 292 Grassmann product 6 exterior algebra 6, 30 117, 137, 140, 148, 195, Grassmann, Hermann Giinther 5, 24 207, 213, 282, 291 Grassmann, Th eory of Ext ension 5 exterior algebra fields, equivalence classes of Graves-Morris algorithm 343, 348 177 Graves-Morris, generalized inverse rational exterior algebra, complexification of 207 forms of 346 exterior algebra, grade involution in 141 exterior algebra, Poin care automorphism of H. 196 Hahn-Ban ach theorem 336 exterior algebra, quantizat ion of 398 Hamilt on, William Rowan 4, 10, 24, 265 exteri or algebra, reversion in 141 Hardy, Godfrey Harold 54 exterior derivative 291 Heeke braid 397, 398, 407, 409 exterior differential forms, Kahler product of Heisenberg group 33 140 Hermite interpolants 343, 353 exterior exponential of a bivector 140 Hermite polynomial, vector-valued 356 exterior product , of vector spaces x, 29 Higgs mechanism 282,297,298 Hodge *-operator 291, 366, 370 F. homomorphism between Spin+(p, q) and Fierz identities 153, 154, 162, 193 SO+(p, q) 179, 181 Fierz mult ivector 155 Hopf algebra 266 finite Dirac group 61, 70 Hurwitz pairs 24, 387 finite Dirac group, irreducible representations Hurwitz, probl em 387 61,71 Huygens principle 302, 305 finite Dirac groups, typ es of 77 Huygens' integral formulae, conformal covari­ finite geometry over GF(2 ) 59, 62 ance of 301 finite geometry table 69, 72 hyperbolic space 41, 56, 193, 194 form, alternating 146 hyperbolic space, of constant sectional curva­ form, symmetric, non-singular 32 ture 251 functions, biregular 326 hypervolume 134 functions, hoIomorphic 301, 307 functions, monogenic 303, 313, 320, 335, 339 I. functions, regular 319, 326 ideal, minimal 113, 125, 131 417

idempotent, central 71, 119, 121 Laplace operator, Dirichlet eigenvalues of 248 idempotent, primitive xii, 113, 118, 138, 149, left (right) conjugate of a vector space 114 178,180, 181, 182 left-invariant vector fields on Spin(n) -bundle idempotents, lifting of 113, 122 367,369,375 idempotents, mutually annihilating 81, 84, Lichnerowicz, Andre ix 102, 103, 107, 117 line, hyperbolic 60, 75 idempotents, primitive, in C£1 ,3 180, 181 line, self-polar 75, 93 idempotents, primitive, in C£4,1 182 linear operator 101, 103, 107 inertial frame 10, 16 Lipschitz group 140, 349 inhomogeneous group, acting on a vector bun­ Lorentz boost 10, 16, 21, 128 dle 259 Lorentz boost, orthogonal 293 interactions, fermionic and bosonic 199 Lorentz boost, pure 261 interior product of Cartan 144 Lorentz group 10, 15, 17, 169 intrinsic conjugation of spinors 205, 208, 232, Lorentz group, discrete transformations in 293 234 Lorentz group, parity operator in 23 isometry classes of anisotropic quadratic forms Lorentz group, representations of 8, 23, 291 140 Lorentz group, restricted 129, 171 isotropic r-vector 120 Lorentz transformations 8, 10, 16, 21, 26, 125, isotropic tangent vector fields 200 128, 161, 172,291 Lorentzian manifold 177, 186, 187 J. Lorentzian manifold, second Stiefel-Whitney Jacobi identity 22 class of 188 Jordan basis 106 Lorentzian manifold, spinor structure of 187 Jordan chain 101, 103 Levi-Civita tensor 22

K. M. Kaluza-Klein theories 206 Majorana algebra 80 Kelvin inversion 302, 303 manifold, intrinsic metrical geometry of 6 Killing spinors 243, 244, 245, 249, 250, 252 Manin's plane 389 Killing, Wilhelm 10 Markov chains 199 Kirchberg's inequality 252 Markov processes 202 Klein's quadric 96 Mauer-Cartan formula 369 Klein-Gordon equation 8 maximal totally isotropic subspace 113, 137, Kahler manifold 246 163, 193, 202 Kahler product for exterior differential forms Maxwell's equations, biquaternionic formula­ 140 tion of 265 Kahler-Atiyah algebra 140, 380 Maxwell's equations, source-free 322 Kahler-Atiyah isomorphism 141 Maxwell's equations, vector form 267 Kahler-Dirac equation 141 McKane-Parisi-Sourlas theorem 199, 201 Kahler-Killing spinors 252 minimal left ideal 138 Kahler-twister spinors 252 minimal left ideal, nilpotent homogeneous el­ ement of 138 L. minimal left ideals in a matrix algebra 151 Lagrangians, spinor invariance of 293, 294 minimal left ideals, direct sum of 81 Lagrangians, vector invariance of 293 minimal polynomial 101, 105 Lame system in n-dimensions 329 Minkowski space-time 17, 117,265 418 modul e, invertible 42 Pauli matrices 15,20,24,127,170,265 modul e, over exterior algebra AV 141, 148 Penrose's "flag" 134 modul e, proj ective, Witt group of 42 pentads 60 modul e, quadratic 46, 113 physical observables 137, 149, 164 modul e, reflexive 42 physical tensor fields 6 Moisil-Teodorescu transform 326, 339 pin group, Pin(1,3) 161,172,181,281 Moore-Penrose generalized inverse of a vector pin group , Pin(n) 302 344 pin group, Pin(p, q) 179 mother algebra 196 pin group, definition of 161, 179 mother spinor 157, 158, 181, 185 plane, hyperbolic 75, 115 multivector algebra 125, 133 plane , isotropic 75 mutually non-conjugate set (MNCS) 66 plane, metabolic 115 Mobius transformations 301, 302, 307 Plemelj-Sokhotzkij's formula 327 Poincare group 15, 18, 26 N. prin cipal bundl e, of oriented Lorent z tetrads neutrino oscillation 26 186, 187 neutrino wave function, Lagrangian for 298 principal bundl e, of orthonormal frames 192 Noether theorem 295 principal spin bundle 365, 372 Noether-Skolem th eorem 180 principles of relativity 10, 15, 16, 18 non-commutative geometry 365 proj ective geometry PG(n - 1,2) 62 non-commutative spin manifold 375 projective quadric over GF(2) 88 null tetrad 131 null vector 134 Q. quadratic algebra, Chevalley-Kahler deforma­ O. tion of 398 Obata theorem 252 quadratic algebra, quantizati on of 404, 405 off-diagonal set (OS) 66 quadratic form 40, 63, 76, 114 operator, nilpotent 103 quadratic form, degenerate 114 operators, annihilation, creation 257 quadratic form, elliptic and hyperbolic 64 orthogonal geometry 63 quadrati c form , in characteristic 2 50, 145 ort hogonal group over GF(2) 90 quadratic form , neutral 137, 206, 149 orthogonal group, infinite 9 quadrati c form, of Hardy-Weinberg 54 orthogonal subgroups, conjugacy classes of 64 quadratic form , of maxim al rank 68 quadratic form , positive definite 15 P. quadratic form, Witt index of 113, 116 Pad e approximant, generalized inverse 346 quadratic forms, periodicity of 69, 89 Pad e theory 346 quadratic modul es, cat egory of 39 pair, hyperbolic, of isotropic vectors 115 quadratic space, multiplicative structure on pair-wise non-polar set (PNPS) 59, 66 43, 45, 48 paravector 127, 319 quadratic space, neutral 137, 206, 149 paravector function s 315 quadric, k -cap of 89 paravector space, complexification of 127, 314, quadric, elliptic 60, 76, 79, 88, 89 336 quadric, hyperbolic 89 parity grading 137, 141 quadric, parabolic 65, 88 partition of unity 102 quadric, proj ective 65, 75, 77, 82 Pauli algebra 35, 127, 128, 129, 291,313 quadrivector 17 419

quantum braided deformation of IGL(n, R)­ group 391 S. quantum braid ed generators 390 Schrodinger equation 26 quantum braided group 387 Schonberg, Mario xii, 178 quantum braided inhomogeneous general lin­ second Cl!ch cohomology group 189 ear group 389 second fundam ental form 249 quantum braid ed inhomogeneous pseudo­ semi-spinors 35, 119,205, 238 orthogonal group 388 simple k-ve ctors in exterior algebra 141 quantum Clifford algebra 398 simple Clifford algebras, representation mod­ quantum deformation of spinor groups 392 ules of 180 quantum geometry 391 space, anisotropic 115 quantum principal bundl e 365 space, hyperbolic 115 quantum space 387, 388 space, isotropic 115 quantum spaces, spinor structures on 365 space, symplectic 31 quaternion algebra 4, 10, 24, 134 space , totally isotropic 115 quaternion field 180 space-time algebra 24, 133, 180 quaternion formulation of special relativity space-time algebra, complex 160 265 space-time, Riemann-Cartan 186 quaternion, complex 127, 265, 313 space-time, spinor structure of 192 quaternion, norm of 265 special linear group SL(2,C) 20, 125, 126, quaternion , pure 4, 7 130, 168 quaternion , unit 24 spin current tensor 295 quaternionic Kahler manifold 246 spin group 125, 140, 161, 365, 366 quotient bundl e 186, 191 spin group, ,fpin+(1,3) 128,129 spin group , Spin(1,3) 161, 172, 181 R. spin group, Spin(3,1) 281,282,290,297 radical of a vector space 62, 82, 114 spin group, Spin(p, q) 179 Rees algebra 42 spin group , Spin+(1,3) 183, 184, 187, 188, regular function s of biquaternion 313 190, 191 regular functions, exponential 272, 275 spin group, Spin+(4,1) 183, 184 regular functions, polynomial 270, 273 spin group, Spin+(p,q) 183,184,185 regularity condition for functions of a quater­ spin manifold 190 nion 267 spin transformations 129, 131 Riemannian manifold, Clifford multiplication spin-1/2 quantum fields 257 on 243 spinor algebra 3, 8, 26, 35, 125, 205 Riemannian manifold, conformally flat 255 spinor basis 81, 125, 130, 184,202,259 Riemannian manifold , Einstein-Sasakian spinor fibrations 9 structure on 250 spinor fields 174, 177, 178 Riemannian manifold, Laplace operator of 245 spinor group 9, 36, 179 Riemannian manifold, spin bundle on 243 spinor left (right) multiplication 293 Riemannian manifold, twistor spinor on 253 spinor operator 137, 164 Riesz's formula 137 spinor space for Cll ,t 118 Riesz, Marcel 9, 125, 137, 139, 140, 151, 265, spinor space, conjugation on 229, 232, 234 302,307 spinor spaces 210 rings, with minimum condition 113, 120 spinor spaces, inner products on i31, 143,205, Rzewuski, Jan 134 206, 208, 214, 220, 223, 225, 226, 235, 237 420 spinor superfields 177, 197 symplectic geometry, synthemes in 96 spinor transformati ons 35, 125, 168, 205, 208, symplectic group Sp(2m,2) 62 216 symplectic group over GF(2) 90 spinor, adjoint of 134, 150 symplectic manifold 32 spinor, algebraic ix, 160, 183, 199 symplectic space, hyperbolic subspace of 93 spinor, as a column 149, 150, 152 symplectic space, isotropic subspace of 93 spinor, as a matrix 149 symplectic transvection 31, 64, 92 spinor, Clifford algebraic 151, 152 spinor, current density of 151, 152 T. spinor, element of a minimal left ideal 9 tensor algebra 27 spinor, element of a representation space 8 tensor algebra, canonical isomorphisms 29 spinor, handedness of 24, 26 tensor algebra, two-sided ideals in 29, 33 spinor, ideal 158 tensor algebra, universal prop erty of 27, 29, 33 spinor, norm alized 171 tensor , dual 22 spinor, probability density of 151, 152 tensor, rank of 17 spinor, pur e 24, 119, 120, 137, 149, 205, 238, tensor, torsion 186 282 Teodorescu transform 326, 339 spinor, symplectic 9 tetrads 131, 170, 296 spinoriality group ix, 137, 138 tri ads 60 spinors and Kepler motion 151 twisted external algebra 388 spinors, as a graded exterior algebra over null twistor operator 243, 244, 245 spaces 206 twistor space xi, 120, 133, 206, 239 spinors, as columns 164 twist or spinors 243, 244 spinors, as operators 149, 151, 159 twistor, reference 133 spinors, covariant/contravariant 130 twistor, tr anspose 134 spinors, fund amental representations of 173 spinors, harmonic 246 U. spinors, linear tr ansformat ions of 206, 208, unified metric 379 214, 222 unit tensors 379 spinors, local field of 200 unitary group SU(2, C) 168, 170, 297 spinors, positive, negat ive energy 258 spinors, real and complex 149 V. stochastic phenomena 200 Vahlen matrices 301, 302, 303 Stokes ' equations 325, 331, 332 Vahlen, K.Th . 301 SU(2) gauge th eory 298 Van der Waerden, B.L. 240 supercomplex structure 387 Vandermonde matrix, generalized 104 superfields 177, 193 vector algebra 25 supersymmetry xii, 199 vector Claessens' identity 354 SUSY field-theoretical random walk 202 vector epsilon-algorithm 343, 356 Sylvester's th eorem 116 vector field, homotopic deformation of 200 symmetric product , of vector spaces 29 vector Hermite problem, linearized 354 symplectic automorphisms 31 vector Pade approximant 346, 347, 350, 354 symplectic basis 115 vector rotations, as spinor transformations 218 symplectic form 31 vector space, metabolic 115 symplectic geometry 32, 62, 66 vector space, neutral 116 symplectic geometry, duality 96 vector space, of maximum Witt index 116 421 vector spaces, transformations of 167, 172 vector valued functions, rational approxi­ mants to 343, 345 vectors, exterior product of x, 29 vectors , scalar product of

W. Weitzenbok formulas 245 Weyl algebra z, 27, 33, 398, 409 Weylspinorl5, 24, 26, 137, 138, 149, 162, 239, 291 Weyl spinor, as pure spinor 162 Weyl spinor, charge conjugated 162 Weyl spinor, covariants of 162 Weyl spinor, helicity of 162 Weyl spinor, in operator form 162 Weyl's equation 291 Weyl's 'coordinatization' program 298 Weyl, Hermann 9, 214 Weyl-Heisenberg algebra 410 Wigner rotation 261 Wigner time reversal 161 Witt basis 193, 197, 202 Witt decomposition 9, 113, 115, 120 Witt ring 42, 140 Witt theorem 115 Witt, E. 140 Y. Yamabe operator 246 Yamabe problem 254 Yang-Baxter algebra 408 Yang-Baxter category 388 Yang-Baxter condition 389 Yang-Baxter equation 387 Yvon-Takabayashi angle 186

Z. Zamolodchikov algebra 408 Zariski topology 40 Other Mathematics and Its Applications titles of interest:

P.H. Sellers: Combinatorial Complexes. A Mathematical Theory of Algorithms. 1979,200 pp. ISBN 90-277-1000-7 P.M. Cohn: Universal Algebra. 1981, 432 pp. ISBN 90-277-1213- 1 (hb), ISBN 90-277-1254-9 (ph, J. Mockor: Groups ofDivisibility. 1983, 192 pp. ISBN 90-277-1539-4 A Wwarynczyk: Group Representations and Special Functions. 1986, 704 pp. ISBN 90-277-2294-3 (ph), ISBN 90-277-1269-7 (hh) I. Bucur: Selected Topics in Algebra and its Interrelations with Logic, Number Theory and Algebraic Geometry. 1984,416 pp. ISBN 90-277-1671-4 H. Walther: Ten Applications ofGraph Theory. 1985,264 pp. ISBN 90-277-1599-8 L. Beran: Orthomodular Lattices. Algebraic Approach. 1985,416 pp. ISBN 90-277-1715-X A Pazman: Foundations ofOptimum Experimental Design. 1986, 248 pp. ISBN 90-277-1865-2 K. Wagner and G. Wechsung: Computational Complexity. 1986,552 pp. ISBN 90-277-2146-7 AN. Philippou, G.E. Bergum and AF. Horodam (OOs.): Fibonacci Numbers and Their Applications. 1986,328 pp. ISBN 90-277-2234-X C. Nastasescu and F. van Oystaeyen: Dimensions ofRing Theory. 1987,372 pp. ISBN 9O-277-2461-X Shang-Ching Chou: Mechanical Geometry Theorem Proving. 1987,376 pp. ISBN 90-277-2650-7 D. Przeworska-Rolewicz: Algebraic Analysis. 1988,640 pp. ISBN 90-277-2443-1 C.T.J. Dodson: Categories, Bundles and Spacetime Topology. 1988,264 pp. ISBN 90-277-2771-6 V.D. Goppa: Geometry and Codes. 1988, 168 pp. ISBN 90-277-2776-7 AA Markov and N.M. Nagorny: The Theory ofAlgorithms. 1988,396 pp. ISBN 90-277-2773-2 E. Kratzel: Lattice Points. 1989,322 pp. ISBN 90-277-2733-3 A.M.W. Glass and W.Ch. Holland (OOs.): Lattice-Ordered Groups. Advances and Techniques . 1989,400 pp. ISBN 0-7923-0116-1

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