On root categories of finite-dimensional algebras

JOURNAL OF ALGEBRA

卷:370

Article

Fu, Changjian

关键词: Root category;    Ringel-Hall Lie algebra;    GIM-Lie algebra;   

DOI  :  10.1016/j.jalgebra.2012.07.037

来源: Elsevier

【 摘 要 】

For any finite-dimensional algebra A over a field k of finite global dimension, we investigate the root category R-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 of global dimension 2, which turns out to give an alternative answer to a question of GIM-Lie algebras by Slodowy in Beyond Kac-Moody algebra, and inside. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free