Gelfand-Fuchs cohomology for affine superspaces A^(m,n)
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911810784854016 |
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| author | Pimenov, Slava |
| author_facet | Pimenov, Slava |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gelfand-Fuchs cohomology for affine superspaces A^(m,n) Pimenov, Slava Algebraic Geometry Representation Theory 17B56 (Primary), 17B66 (Secondary) 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. |
| title | Gelfand-Fuchs cohomology for affine superspaces A^(m,n) |
| topic | Algebraic Geometry Representation Theory 17B56 (Primary), 17B66 (Secondary) |
| url | https://arxiv.org/abs/2403.15868 |