Deformation cohomology of Lie algebroids and Morita equivalence

Giovanni Sparano; Luca Vitagliano

doi:10.1016/j.crma.2018.03.004

Homological algebra/Differential geometry

Deformation cohomology of Lie algebroids and Morita equivalence
[Cohomologie de déformation d'un algèbroïde de Lie et équivalence de Morita]

Présenté par : the Editorial Board

Giovanni Sparano ¹ ; Luca Vitagliano ¹

¹ DipMat, Università degli Studi di Salerno, via Giovanni Paolo II n

Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 376-381.

Résumé
Abstract

Soit $A \Rightarrow M$ un algébroïde de Lie. Dans cette note, nous prouvons qu'un pull-back de A lelong d'une fibration ayant des fibres homologiquement m-connexes possède la même cohomologie de déformation que A jusqu'au degré m.

Let $A \Rightarrow M$ be a Lie algebroid. In this short note, we prove that a pull-back of A along a fibration with homologically m-connected fibers shares the same deformation cohomology of A up to degree m.

Reçu le : 2018-01-30
Accepté le : 2018-03-09
Publié le : 2018-03-19

DOI : 10.1016/j.crma.2018.03.004

Affiliations des auteurs :

Giovanni Sparano ¹ ; Luca Vitagliano ¹

¹ DipMat, Università degli Studi di Salerno, via Giovanni Paolo II n

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     title = {Deformation cohomology of {Lie} algebroids and {Morita} equivalence},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {376--381},
     publisher = {Elsevier},
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     number = {4},
     year = {2018},
     doi = {10.1016/j.crma.2018.03.004},
     language = {en},
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Giovanni Sparano; Luca Vitagliano. Deformation cohomology of Lie algebroids and Morita equivalence. Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 376-381. doi : 10.1016/j.crma.2018.03.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.03.004/

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