Quivers with relations arising from Koszul algebras of $\mathfrak{g}$-invariants

Abstract

Let $\mathfrak{g}$ be a complex simple Lie algebra and let $\Psi$ be an extremal set of positive roots. One associates with $\Psi$ an infinite dimensional Koszul algebra $\bold S_Ψ^{\lie g}$ which is a graded subalgebra of the locally finite part of $((\bold V)^{op}\tensor S(\lie g))^{\lie g}$, where $\mathbf{V}$ is the direct sum of all simple finite dimensional $\lie g$-modules. We describe the structure of the algebra $\bold S_Ψ^{\lie g}$ explicitly in terms of an infinite quiver with relations for $\lie g$ of types $A$ and $C$. We also describe several infinite families of quivers and finite dimensional algebras arising from this construction.

49 pages, AMSLaTeX+amsrefs

References in corpus (3)

• The restricted Kirillov-Reshetikhin modules for the current and twisted current algebras
• Current algebras, highest weight categories and quivers
• A family of Koszul algebras arising from finite-dimensional representations of simple Lie algebras

Cited by in corpus (1)

• A family of Koszul algebras arising from finite-dimensional representations of simple Lie algebras