Hall algebras associated to triangulated categories, II: almost associativity
Representation Theory
2010-01-25 v3 Rings and Algebras
Abstract
By using the approach in \cite{XX2006} to Hall algebras arising in homologically finite triangulated categories, we find an `almost' associative multiplication structure for indecomposable objects in a 2-periodic triangulated category. As an application, we give a new proof of the theorem of Peng and Xiao in \cite{PX2000} which provides a way of realizing symmetrizable Kac-Moody algebras and elliptic Lie algebras via 2-periodic triangulated categories.
Keywords
Cite
@article{arxiv.0710.5588,
title = {Hall algebras associated to triangulated categories, II: almost associativity},
author = {Fan Xu},
journal= {arXiv preprint arXiv:0710.5588},
year = {2010}
}
Comments
15 pages