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arXiv · 2403.15868

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

Slava Pimenov
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Abstract

We study the cohomology of Lie superalgebra of vector fields on affine super-spaces $\mathbb{A}^{m,n}$ 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 $m \geq n$. 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 $\mathfrak{gl}(m,n)$ with coefficients given by Schur functors of the standard representation.

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Slava Pimenov. 2024-03-23. Gelfand-Fuchs cohomology for affine superspaces A^(m,n). https://arxiv.org/abs/2403.15868

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