ORCID Identifier(s)

0000-0001-7556-5346

Graduation Semester and Year

2022

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Dimitar Grantcharov

Abstract

Representation theory of Lie algebra of a finite dimensional reductive Lie algebra g is a long-standing problem. The ultimate goal is to classify all representations of g. However. the only case only case when a complete classification is obtained is the case of g = sl(2). Hence, it is natural to study certain categories of representations of g for which some finiteness conditions on the action of certain elements of g is enforced. In this thesis, we introduce a class of representations T (g, V, S) of sl(n + 1) of mixed tensor type. By varying the polynomial g, the gl(n)-module V , and the set S, we obtain important classes of weight representations over the Cartan subalgebra h of sl(n + 1), and representations that are free over h. Moreover, An isomorphism theorem and simplicity criterion for T(g,V,S) is provided.

Keywords

Lie algebras, Representation theory

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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