GENERALIZED MCKAY QUIVERS, ROOT SYSTEM AND KAC-MOODY ALGEBRAS

DOI10.4134/JKMS.2015.52.2.239zbMATH Open1335.16011arXiv1102.3951OpenAlexW2962810294MaRDI QIDQ5179503

Bo Hou, Shilin Yang

Publication date: 20 March 2015

Published in: Journal of the Korean Mathematical Society (Search for Journal in Brave)

Abstract: Let $Q$ be a finite quiver and $GsubseteqAut(mathbbmkQ)$ a finite abelian group. Assume that $hatQ$ and $Gamma$ is the generalized Mckay quiver and the valued graph corresponding to $(Q,G)$ respectively. In this paper we discuss the relationship between indecomposable $hatQ$-representations and the root system of Kac-Moody algebra $mathfrakg(Gamma)$. Moreover, we may lift $G$ to $$ such that $mathfrakg(Gamma)$ embeds into the fixed point algebra $$ and $$ as $mathfrakg(Gamma)$-module is integrable.

Full work available at URL: https://arxiv.org/abs/1102.3951

zbMATH Keywords

Kac-Moody algebrasroot systemsindecomposable representationsrepresentations of quiversskew group algebrasgeneralized McKay quivers

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Representations of quivers and partially ordered sets (16G20) Root systems (17B22)

Related Items (4)

Absolutely indecomposable representations and Kac-Moody Lie algebras. (With an appendix by Hiraku Nakajima). ⋮ ALGEBRA PAIRS ASSOCIATED TO McKAY QUIVERS ⋮ McKay quivers and Lusztig algebras of some finite groups ⋮ The duality of Auslander-Reiten quiver of path algebras

This page was built for publication: GENERALIZED MCKAY QUIVERS, ROOT SYSTEM AND KAC-MOODY ALGEBRAS

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5179503)