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
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Nguyen, Khoa Hoang, "Exponential Tensor Modules" (2022). Mathematics Dissertations. 227.
https://mavmatrix.uta.edu/math_dissertations/227
Comments
Degree granted by The University of Texas at Arlington