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arXiv · 1409.6803

A Hopf algebra associated to a Lie pair

Zhuo Chen·Mathieu Stiénon·Ping Xu
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Abstract

The quotient $L/A[-1]$ of a pair $A\hookrightarrow L$ of Lie algebroids is a Lie algebra object in the derived category $D^b(\mathscr{A})$ of the category $\mathscr{A}$ of left $\mathcal{U}(A)$-modules, the Atiyah class $\alpha_{L/A}$ being its Lie bracket. In this note, we describe the universal enveloping algebra of the Lie algebra object $L/A[-1]$ and we prove that it is a Hopf algebra object in $D^b(\mathscr{A})$.

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BibTeXRIS

Zhuo Chen, Mathieu Stiénon, Ping Xu. 2014-09-24. A Hopf algebra associated to a Lie pair. https://doi.org/10.1016/j.crma.2014.09.010

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