On root categories of finite-dimenisonal algebras

Abstract

For any finite-dimensional algebra $A$ over a field $k$ with finite global dimension, we investigate the root category $\cR_A$ as the triangulated hull of the 2-periodic orbit category of $A$ via the construction of B. Keller in "On triangulated orbit categories". This is motivated by Ringel-Hall Lie algebras associated to 2-periodic triangulated categories. As an application, we study the Ringel-Hall Lie algebras for a class of finite-dimensional $k$-algebras with global dimension 2, which turn out to give an alternative answer for a question of GIM Lie algebras by Slodowy in "Beyond Kac-Moody algebra, and inside".

25 pages

References in corpus (3)

• On triangulated orbit categories
• Matrix Factorizations and Representations of Quivers I
• The Ringel--Hall Lie algebra of a spherical object

Cited by in corpus (3)

• The Ringel--Hall Lie algebra of a spherical object
• Tilting objects in periodic triangulated categories
• A note on Grothendieck groups of periodic derived categories