Hall algebras associated to triangulated categories, II: almost associativity

2007/10/30 by Fan Xu, Xu, Fan
Mathematics · #16G20 #17B67 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16G20 #msc:17B67

paper · pdf · doi:10.48550/arxiv.0710.5588

15 pages

openalex publication_date 2007/10/30 · arxiv created 2010/01/25 · arxiv updated 2010/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

By using the approach in \citeXX2006 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 \citePX2000 which provides a way of realizing symmetrizable Kac-Moody algebras and elliptic Lie algebras via 2-periodic triangulated categories.

Related

• Hall algebras for odd periodic triangulated categories
• From triangulated categories to Lie algebras: A theorem of Peng and Xiao
• Counting in Calabi--Yau categories, with applications to Hall algebras and knot polynomials
• Hall algebras associated to triangulated categories
• Hall algebras of extriangulated categories