Gelfand-Fuchs cohomology for affine superspaces $\mathbb{A}^{m,n}$
Abstract
We study the cohomology of Lie superalgebra of vector fields on affine super-spaces 𝔸 m,n with trivial coefficients.In this paper we extend the methodology developed in our previous work ([14]) to perform the calculation for arbitrary dimensions (m, n) with m ≥ n.Combined with previously known results for other dimensions (m, n), this 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 𝔤𝔩(m, n) with coefficients given by Schur functors of the standard representation.
Fields of Study & Subjects
Advanced Topics in Algebra
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Beijing Journal of Pure and Applied Mathematics
- Volume
- 3
- Issue
- 1
- Pages
- 121–141
- Publication date
- 1 January 2026
- Language
- EN