2016/12/23 by Kai Behrend, Pooya Ronagh · 5 citations
Mathematics · #Action (physics) #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Filtered algebra #Filtration (mathematics) #Graded Lie algebra #Homotopy and Cohomology in Algebraic Topology #Indecomposable module #Lie algebra #Operator (biology) #Order (exchange) #math.AG #math.QA #msc:14N35 #msc:16G20 #msc:17B37
paper · pdf · doi:10.1112/s0010437x18007881
published in Compositio Mathematica 155(3), 528-598 (Cambridge University Press) · Version 2: polished the paper a bit
openalex created_date 2016/12/16 · arxiv created 2016/12/23 · openalex publication_date 2019/03/01 · arxiv updated 2019/03/27 · openalex updated_date 2026/08/05
We study the action of the inertia operator on the motivic Hall algebra and prove that it is diagonalizable. This leads to a filtration of the Hall algebra, whose associated graded algebra is commutative. In particular, the degree 1 subspace forms a Lie algebra, which we call the Lie algebra of virtually indecomposable elements, following Joyce. We prove that the integral of virtually indecomposable elements admits an Euler characteristic specialization. In order to take advantage of the fact that our inertia groups are unit groups in algebras, we introduce the notion of algebroid .