Quivers and Lie superalgebras

Abstract

Indecomposable representations of quivers are in 1–1 correspondence with positive weight vectors of Kac-Moody algebras. The collection of indecomposable representations of the quiver is tame if the quiver corresponds to a Kac-Moody algebra of polynomial growth. What corresponds to positive roots of Lie algebras of polynomial growth different from Kac-Moody algebras? The classification problem for tame representations of quivers associated to Lie superalgebras is a natural step towards the answer to this question. As an aside we announce a classification of simple graded Lie superalgebras of polynomial growth.