HALL ALGEBRAS ASSOCIATED TO TRIANGULATED CATEGORIES, II: ALMOST ASSOCIATIVITY
By using the approach in (8) to Hall algebras arising in homologi- cally finite triangulated categories, we find an 'almost' associative multiplica- tion 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 (5) which provides a way of realizing symmetrizable Kac-Moody algebras and elliptic Lie algebras via 2-periodic triangulated categories.