The Ringel--Hall Lie algebra of a spherical object

Abstract

For an integer $w$, let $\cs_w$ be the algebraic triangulated category generated by a $w$-spherical object. We determine the Picard group of $\cs_w$ and show that each orbit category of $\cs_w$ is triangulated and is triangle equivalent to a certain orbit category of the bounded derived category of a standard tube. When $n=2$, the orbit category $\cs_w/Σ^2$ is 2-periodic triangulated, and we characterize the associated Ringel--Hall Lie algebra in the sense of Peng and Xiao.

26pages

References in corpus (4)

• On triangulated orbit categories
• On root categories of finite-dimenisonal algebras
• On a triangulated category which behaves like a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon
• Hall algebras for odd periodic triangulated categories

Cited by in corpus (4)

• Derived categories of graded gentle one-cycle algebras
• Fourier-Mukai functors in the supported case
• Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
• On root categories of finite-dimenisonal algebras