On Morita Equivalences Between KLR Algebras and VV Algebras

Walker, Ruari (2016) On Morita Equivalences Between KLR Algebras and VV Algebras. Doctoral thesis, University of East Anglia.

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Abstract

This thesis is investigative work into the properties of a recently de�ned family of graded algebras,
which we call VV algebras. These algebras were de�ned by Varagnolo and Vasserot.
We compare categories of modules over KLR algebras with categories of modules over VV
algebras, establishing various Morita equivalences. Using these Morita equivalences we are
able to prove several properties of certain classes of VV algebras such as a�ne cellularity
and a�ne quasi-heredity. We also include a discussion about the problems encountered
when trying to de�ne �nite-dimensional quotients of these algebras. Finally, in certain
settings, we show how to de�ne these quotients and explain how they relate to cyclotomic
KLR algebras.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Mia Reeves
Date Deposited: 04 May 2016 09:20
Last Modified: 04 May 2016 09:20
URI: https://ueaeprints.uea.ac.uk/id/eprint/58559
DOI:

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