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F-algebroids and
deformation quantization via pre-Lie algebroids
John Alexander Cruz Morales, Jiefeng Liu and Yunhe Sheng |
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Vol. 326 (2023), No. 2, 251–284
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Abstract |
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First we introduce the notion of F-algebroids, which is a generalization of F-manifold algebras and F-manifolds, and show that F-algebroids are the corresponding semiclassical limits of pre-Lie formal deformations of commutative associative algebroids. Then we use the deformation cohomology of pre-Lie algebroids to study pre-Lie infinitesimal deformations and extension of pre-Lie n-deformations to pre-Lie (n+1)-deformations of a commutative associative algebroid. Next we develop the theory of Dubrovin’s dualities of F-algebroids with eventual identities and use Nijenhuis operators on F-algebroids to construct new F-algebroids. Finally we introduce the notion of pre-F-algebroids, which is a generalization of F-manifolds with compatible flat connections. Dubrovin’s dualities of pre-F-algebroids with eventual identities, Nijenhuis operators on pre-F-algebroids are discussed. |
Keywords
F-algebroids, pre-F-algebroids, eventual identity,
Nijenhuis operator
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Mathematical Subject Classification
Primary: 53D17, 53D45, 53D50, 53D55
Secondary: 14J33
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Milestones
Received: 11 August 2022
Revised: 20 November 2023
Accepted: 22 November 2023
Published: 9 January 2024
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Authors |
| John Alexander Cruz Morales | |
| Max Planck Institute for
Mathematics Bonn Germany |
Departamento de matemáticas Universidad Nacional de Colombia Bogotá Colombia |
| Jiefeng Liu | |
| School of Mathematics and
Statistics Northeast Normal University Jilin China |
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| Yunhe Sheng | |
| Department of Mathematics Jilin University Jilin China |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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