Gelfand-Fuchs cohomology for affine superspaces A^(n,1)

Abstract

We study the cohomology of Lie superalgebra of vector fields on affine super-spaces ${\mathbb{A}}^{m,n}$ with trivial coefficients. Previously known results covered the classical case ${\mathbb{A}}^m={\mathbb{A}}^{m,0}$ as well as the case ${\mathbb{A}}^{m,n}$ with $m\le n$. In this paper we perform the computation for super-spaces ${\mathbb{A}}^{m,1}$.

15 pages