On root categories of finite-dimenisonal algebras

2011/03/17 by Changjian Fu · 1 citation
Mathematics · #math.RA #math.RT #msc:16D90 #msc:17B67 #msc:18E30

paper · pdf · doi:10.1016/j.jalgebra.2012.07.037

published as Journal of Algebra 370(2012) 233-265 · 25 pages

arxiv created 2011/03/17 · arxiv updated 2018/09/11

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".

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• Singularity categories of representations of algebras over local rings

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