| Reference : Atiyah classes and dg-Lie algebroids for matched pairs |
| Scientific journals : Article | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/29497 | |||
| Atiyah classes and dg-Lie algebroids for matched pairs | |
| English | |
| Batakidis, Panagiotis [> >] | |
Voglaire, Yannick  [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |
| 2017 | |
| Journal of Geometry and Physics | |
| Elsevier Science | |
| Yes (verified by ORBilu) | |
| International | |
| 0393-0440 | |
| Amsterdam | |
| The Netherlands | |
| [en] differential graded manifolds ; Atiyah classes ; Lie algebroids ; Fedosov resolutions | |
| [en] For every Lie pair $(L,A)$ of algebroids we construct a dg-manifold structure on the $\ZZ$-graded manifold $\M=L[1]\oplus L/A$ such that the inclusion $\iota: A[1] \to \M$ and the projection $p:\M\to L[1]$ are morphisms of dg-manifolds.
The vertical tangent bundle $T^p\M$ then inherits a structure of dg-Lie algebroid over $\M$. When the Lie pair comes from a matched pair of Lie algebroids, we show that the inclusion $\iota$ induces a quasi-isomorphism that sends the Atiyah class of this dg-Lie algebroid to the Atiyah class of the Lie pair. We also show how (Atiyah classes of) Lie pairs and dg-Lie algebroids give rise to (Atiyah classes of) dDG-algebras. | |
| Researchers | |
| http://hdl.handle.net/10993/29497 | |
| 10.1016/j.geomphys.2017.08.012 | |
| http://arxiv.org/abs/1601.06254 |
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