A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917233504026624 |
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| author | Billig, Yuly Ingalls, Colin |
| author_facet | Billig, Yuly Ingalls, Colin |
| contents | We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in étale charts these associative algebras decompose into a tensor product of the algebra of differential operators and the universal enveloping algebra of the Lie algebra of power series vector fields vanishing at the origin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07918 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties Billig, Yuly Ingalls, Colin Representation Theory Algebraic Geometry 17B66 (Primary) 14F10 (Secondary) We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in étale charts these associative algebras decompose into a tensor product of the algebra of differential operators and the universal enveloping algebra of the Lie algebra of power series vector fields vanishing at the origin. |
| title | A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties |
| topic | Representation Theory Algebraic Geometry 17B66 (Primary) 14F10 (Secondary) |
| url | https://arxiv.org/abs/2302.07918 |