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

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

2008-10-08

arxiv.org/abs/0810.1532v1

J. Algebra 322 (2009), no. 12, 4430-4478

Mathematics

Representation Theory

49 pages, AMSLaTeX+amsrefs

Scientific paper

10.1016/j.jalgebra.2009.09.032

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 $\bold S_\Psi^{\lie g}$ which is a graded subalgebra of the locally finite part of $((\bold V)^{op}\tensor S(\lie g))^{\lie g}$, where $\bold V$ is the direct sum of all simple finite dimensional $\lie g$-modules. We describe the structure of the algebra $\bold S_\Psi^{\lie g}$ 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.

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