Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 12-2017 Real Simple Lie Algebras: Cartan Subalgebras, Cayley Transforms, and Classification Hannah M. Lewis Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Mathematics Commons Recommended Citation Lewis, Hannah M., "Real Simple Lie Algebras: Cartan Subalgebras, Cayley Transforms, and Classification" (2017). All Graduate Theses and Dissertations. 6900. https://digitalcommons.usu.edu/etd/6900 This Thesis is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact
[email protected]. REAL SIMPLE LIE ALGEBRAS: CARTAN SUBALGEBRAS, CAYLEY TRANSFORMS, AND CLASSIFICATION by Hannah M Lewis A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Mathematics Approved: Ian Anderson, Ph.D. Mark Fels, Ph.D. Major Professor Committee Member Nathan Geer, Ph.D. Mark McLellan, Ph.D. Committee Member Vice President for Research and Dean of the School of Graduate Studies UTAH STATE UNIVERSITY Logan, Utah 2017 ii Copyright c Hannah M Lewis 2017 All Rights Reserved iii Abstract Real Simple Lie Algebras: Cartan Subalgebras, Cayley Transforms, and Classification by Hannah M. Lewis, Master of Science Utah State University, 2017 Major Professor: Dr. Ian Anderson Department: Mathematics and Statistics The differential geometry software package in Maple has the necessary tools and commands to automate the classification process for complex simple Lie algebras. The purpose of this thesis is to automate the classification process for real simple Lie alge- bras.