Vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair
| Autor: | Chang, Hua-Shin, Liao, Hsuan-Yi |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We investigate vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair $(L,A)$, i.e. a pair of a Lie algebroid $L$ and a Lie subalgebroid $A$ of $L$. The construction of Fedosov dg manifolds involves a choice of a splitting and a connection. We prove that, given any two choices of a splitting and a connection, there exists a unique vertical isomorphism, determined by an iteration formula, between the two associated Fedosov dg manifolds. As an application, we provide an explicit formula for the map $\mathrm{pbw}_2^{-1}\circ \mathrm{pbw}_1$ associated with two Poincar\'{e}--Birkhoff--Witt isomorphisms that arise from two choices of a splitting and a connection. Comment: 22 pages. Minor revision; some terminologies changed; some proofs improved. To appear in Journal of Geometry and Physics |
| Databáze: | arXiv |
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