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arXiv · 2107.11714

On Lie algebroid over algebraic spaces

Ashis Mandal·Abhishek Sarkar
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Abstract

We consider Lie algebroids over algebraic spaces (in short we call it as $a$-spaces) by considering the sheaf of Lie-Rinehart algebras. We discuss about properties of universal enveloping algebroid $\mathscr{U}(\mathcal{O}_X,\mathcal{L})$ of a Lie algebroid $\mathcal{L}$ over an $a$-space $(X, \mathcal{O}_X)$. This is done by sheafification of the presheaf of universal enveloping algebras for Lie-Rinehart algebras. We review the extent to which structure of the universal enveloping algebroid of Lie algebroids (over special $a$-spaces) resembles a sheaf of bialgebras. In the sequel we present a version of Poincar\'e-Birkhoff-Witt theorem and Cartier-Milnor-Moore theorem for the Lie algebroid.

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Ashis Mandal, Abhishek Sarkar. 2021-07-25. On Lie algebroid over algebraic spaces. https://doi.org/10.1080/00927872.2022.2139971

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