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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.01735 |
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Table of Contents:
- We consider Lie algebroids over an algebraic space (or topological ringed space) as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not necessarily of finite rank) as a derived functor, and simplify it via Čech cohomology. Furthermore, we define the Hochschild hypercohomology of a sheaf of generalized bialgebras and study the cases of the universal enveloping algebroid and the jet algebroid of a Lie algebroid. In the sequel, we present a version of Hochschild-Kostant-Rosenberg theorem for a locally free Lie algebroid, as well as its dual version.