Introduced in 2008 by Khovanov and Lauda, and independently by Rouquier, the KLR algebras are a family of infinite-dimensional graded algebras which categorify the negative part of the quantum group associated to a graph. In finite types these algebras are known to have nice homological properties, in particular they are affine quasi-hereditary. In this talk I'll explain what it means to be affine quasi-hereditary and how this relates to properties of finite dimensional algebras. I'll then introduce a finite dimensional quotient of the KLR algebra which preserves some of the homological structure of the original algebra and provide a bound on its finitistic dimension. This work will form part of my PhD thesis, supervised by Dr Vanessa Miemietz.
Properly stratified quotients of Khovanov-Lauda-Rouquier algebras
Keith Brown (UEA)
Mon, 24/11/2014 - 16:30