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Shifted symplectic Lie algebroids

Pym, B., & Safronov, P. (2020). Shifted symplectic Lie algebroids. International Mathematics Research Notices, 2020(21), 7489-7557. doi:10.1093/imrn/rny215.

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https://doi.org/10.1093/imrn/rny215 (Publisher version)
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Creators:
Pym, Brent, Author
Safronov, Pavel1, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201

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Free keywords: Mathematics, Differential Geometry, Algebraic Geometry, Symplectic Geometry
Abstract: Shifted symplectic Lie and $L_\infty$ algebroids model formal neighbourhoods of manifolds in shifted symplectic stacks, and serve as target spaces for twisted variants of classical AKSZ topological field theory. In this paper, we classify zero-, one- and two-shifted symplectic algebroids and their higher gauge symmetries, in terms of classical geometric "higher structures", such as Courant algebroids twisted by $\Omega^2$-gerbes. As applications, we produce new examples of twisted Courant algebroids from codimension-two cycles, and we give symplectic interpretations for several well known features of higher structures (such as twists, Pontryagin classes, and tensor products). The proofs are valid in the $C^\infty$, holomorphic and algebraic settings, and are based on a number of technical results on the homotopy theory of $L_\infty$ algebroids and their differential forms, which may be of independent interest.

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Language(s): eng - English
Dates: 2020
Publication Status: Published in print
Pages: 69
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Rev. Type: Peer
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Degree: -

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Title: International Mathematics Research Notices
Abbreviation : IMRN
Source Genre: Journal
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Publ. Info: Oxford University Press
Pages: - Volume / Issue: 2020 (21) Sequence Number: - Start / End Page: 7489 - 7557 Identifier: -