On Morita Equivalences Between KLR Algebras and VV Algebras
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.
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