Derived Categories and Lie Algebras

2006/04/26 by Jie Xiao, Fan Xu, Xiao, Jie +3
Mathematics · Physics and Astronomy · #16G10 #17B37 #18E30 #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Computer science #Construct (python library) #Dimension (graph theory) #FOS: Mathematics #Lie algebra #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Algebra (math.QA) #Term (time) #math.QA #msc:16G10 #msc:17B37 #msc:18E30

paper · pdf · doi:10.48550/arxiv.math/0604564

40 pages

openalex publication_date 2006/04/26 · arxiv created 2010/01/27 · arxiv updated 2010/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \md^b(A) be the derived category of a finite dimensional basic algebra A with finite global dimension. We construct the Lie algebra arising from the 2-periodic version \mk₂(∓(A)) of \mk^b(∓(A)) in term of constructible functions on varieties attached to \mk₂(∓(A)).

Citations

• Sheaves in Topology
• Cohomology of Sheaves
• Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)
• Quiver varieties and Kac-Moody algebras
• Hall algebras and quantum groups
• COXETER FUNCTORS AND GABRIEL'S THEOREM
• Representation Theory of Artin Algebras
• Tame-wild dichotomy for derived categories
• On triangulated orbit categories

Related

• On root categories of finite-dimenisonal algebras
• Lie algebras arising from two-periodic projective complex and derived categories
• Derived category and Lie algebras
• From triangulated categories to Lie algebras: A theorem of Peng and Xiao
• The 1-periodic derived category of a gentle algebra : Part 1 -- Indecomposable objects