Hall algebras associated to triangulated categories, II: almost associativity

Details Hall algebras associated to triangulated categories, II: almost associativity Hall algebras associated to triangulated categories, II: almost associativity

2007-10-30

arxiv.org/abs/0710.5588v3

Mathematics

Representation Theory

15 pages

Scientific paper

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.

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