From triangulated categories to Lie algebras: A theorem of Peng and Xiao

2005/02/18 by Andrew Hubery, Hubery, Andrew
Mathematics · #16G20 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT #msc:16G20 #msc:18E30

paper · pdf · doi:10.48550/arxiv.math/0502403

arxiv created 2005/02/18 · openalex publication_date 2005/02/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a simplified and more intuitive proof of a theorem of Peng and Xiao, which constructs a Lie algebra from any 2-periodic triangulated k-category (satisfying some finiteness assumptions).

Related

• Hall algebras associated to triangulated categories, II: almost associativity
• On root categories of finite-dimenisonal algebras
• Hall algebras for odd periodic triangulated categories
• Derived Categories and Lie Algebras
• The triangulated hull of periodic complexes