$A_\infty$ Algebras from Lie Pairs
| Autor: | Stiénon, Mathieu, Vitagliano, Luca, Xu, Ping |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given an inclusion $A\to L$ of Lie algebroids sharing the same base manifold $M$, i.e. a Lie pair, we prove that the space $\Gamma(\Lambda^\bullet A^\vee)\otimes_{C^\infty(M)} \frac{U(L)}{U(L)\cdot\Gamma(A)}$ admits a natural $A_\infty$ algebra structure. This $A_\infty$ algebra structure is inherited, by homotopy transfer, from the universal enveloping algebra of the differential graded Lie algebroid arising as the pullback of the Lie algebroid $L\to M$ through the canonical surjective submersion $A[1]\to M$. Comment: 34 pages |
| Databáze: | arXiv |
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