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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.02826 |
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| _version_ | 1866917608825028608 |
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| author | Chang, Hua-Shin Liao, Hsuan-Yi |
| author_facet | Chang, Hua-Shin Liao, Hsuan-Yi |
| contents | 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 Poincaré--Birkhoff--Witt isomorphisms that arise from two choices of a splitting and a connection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02826 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair Chang, Hua-Shin Liao, Hsuan-Yi Differential Geometry Quantum Algebra 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 Poincaré--Birkhoff--Witt isomorphisms that arise from two choices of a splitting and a connection. |
| title | Vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair |
| topic | Differential Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2309.02826 |