2024/03/23 by Slava Pimenov, Pimenov, Slava
Mathematics · #17B56 (Primary) #17B66 (Secondary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2403.15868
openalex publication_date 2024/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the cohomology of Lie superalgebra of vector fields on affine super-spaces \mathbbAm,n with trivial coefficients. In this paper we extend the methodology developed in the previous paper (arXiv:2210.16585) to perform the calculation for arbitrary dimensions (m, n) with m ≥ n. This combined with previously known results for other dimensions (m, n) fully settles the local problem of Gelfand-Fuchs cohomology with trivial coefficients for super-manifolds. As part of the proof we also compute the cohomology of Lie superalgebras \mathfrakgl(m,n) with coefficients given by Schur functors of the standard representation.