Date of Completion
5-3-2016
Embargo Period
4-29-2016
Keywords
Representation Theory, KLR Algebras
Major Advisor
Kyu-Hwan Lee
Associate Advisor
Ralf Schiffler
Associate Advisor
Jerzy Weyman
Field of Study
Mathematics
Degree
Doctor of Philosophy
Open Access
Open Access
Abstract
The module categories of Khovanov-Lauda-Rouquier algebras categorify the integral form of the negative half of the quantum group U_q(g) coming from any symmetrizable Kac-Moody algebra g. We construct a family of simple modules over KLR algebras and show how they can be used to obtain the building blocks of existing classifications of simple finite-dimensional modules in finite types. The construction extends to infinite types, where we obtain simple modules whose structures are easy to describe. We give many explicit examples of this construction in rank 2 cases.
Recommended Citation
Judge, Jonathan Brian, "Modules Over Rank 2 KLR Algebras" (2016). Doctoral Dissertations. 1089.
https://digitalcommons.lib.uconn.edu/dissertations/1089