Hochschild cohomology and lifts of endomorphisms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917417728344064 |
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| author | Lauritzen, Niels Thomsen, Jesper Funch |
| author_facet | Lauritzen, Niels Thomsen, Jesper Funch |
| contents | We study when algebra endomorphisms can be lifted to first-order flat lifts. To a first-order flat lift of an algebra and an endomorphism, we associate a canonical class in Hochschild cohomology with coefficients in a naturally twisted bimodule. The cohomology class vanishes exactly when the endomorphism admits a multiplicative lift.
For an Azumaya algebra of constant rank over a formally smooth center, we prove that an endomorphism lifts if and only if the induced endomorphism of the center preserves the Poisson structure given by the lift of the algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16636 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hochschild cohomology and lifts of endomorphisms Lauritzen, Niels Thomsen, Jesper Funch Rings and Algebras Algebraic Geometry Quantum Algebra We study when algebra endomorphisms can be lifted to first-order flat lifts. To a first-order flat lift of an algebra and an endomorphism, we associate a canonical class in Hochschild cohomology with coefficients in a naturally twisted bimodule. The cohomology class vanishes exactly when the endomorphism admits a multiplicative lift. For an Azumaya algebra of constant rank over a formally smooth center, we prove that an endomorphism lifts if and only if the induced endomorphism of the center preserves the Poisson structure given by the lift of the algebra. |
| title | Hochschild cohomology and lifts of endomorphisms |
| topic | Rings and Algebras Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2604.16636 |