2023/07/20 by Keyou Zeng, Zeng, Keyou
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2307.10545
openalex publication_date 2023/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The well-known Loday-Quillen-Tsygan theorem calculates the Lie algebra homology of the infinite general linear Lie algebra \mathfrakgl(A) over an unital associative algebra A. We generalize the Loday-Quillen-Tsygan theorem to an infinite Lie algebra associated with a (framed) quiver, where we assign to each vertex v an infinite general linear Lie algebra \mathfrakgl(Av), to each edge e an infinite matrix module and to each framed vertex a (anti)-fundamental representation. Given this data, each loop or path ending on framed vertices of the quiver defined a stratified factorization algebra over S1 or [0,1] respectively. We show that the corresponding Lie algebra homology can be expressed as summing the factorization homology over all loops and framed paths of the quiver.