Date of Award:

5-2014

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee Chair(s)

Ian Anderson

Committee

Ian Anderson

Committee

Nathan Geer

Committee

Zhaohu Nie

Abstract

The computer algebra system Maple contains a basic set of commands for working with Lie algebras and matrices. The purpose of this thesis was to extend the functionality of these Maple packages in a number of important areas. First, programs for defining multiplication in several different types of algebras were created to allow users to perform a wider variety of calculations. Second, commands were created for calculating some basic properties of matrix representations of semisimple Lie algebras. This allows a user to identify a given matrix representation by a collection of integers which do not change when the basis of the representation is changed. These integers, called highest weights, uniquely identify the representation. Third, an algorithm was created to allow for a uniform construction of all five exceptional Lie algebras. Maple examples and tutorials are provided to illustrate the implementation and use of the algebras now available in Maple as well as the tools for working with Lie algebra representations.

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