Homotopy <i>G</i>-algebra structure on the cochain complex of hom-type algebras

Apurba Das

doi:10.1016/j.crma.2018.11.001

Algebra/Homological algebra

Homotopy G-algebra structure on the cochain complex of hom-type algebras
[Structure de G-algèbre à homotopie près sur le complexe des co-chaînes des algèbres de type hom]

Présenté par : Michèle Vergne

Apurba Das ¹

¹ Indian Statistical Institute, Kolkata, Stat-Math Unit, 203 BT Road, Kolkata, 700108, India

Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1090-1099.

Résumé
Abstract

Une algèbre hom-associative est une algèbre dont l'associativité est tordue par un homomorphisme d'algèbre. Nous montrons que le complexe des co-chaînes de type Hochschild d'une algèbre hom-associative porte une structure de G-algèbre à homotopie près. Comme conséquence, nous obtenons une structure d'algèbre de Gerstenhaber sur la cohomologie des algèbres hom-associatives. Nous arrivons également à des résultats similaires pour les hom-dialgèbres.

A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. We show that the Hochschild type cochain complex of a hom-associative algebra carries a homotopy G-algebra structure. As a consequence, we get a Gerstenhaber algebra structure on the cohomology of a hom-associative algebra. We also find similar results for hom-dialgebras.

Reçu le : 2018-08-03
Accepté le : 2018-11-06
Publié le : 2018-11-01

DOI : 10.1016/j.crma.2018.11.001

Affiliations des auteurs :

Apurba Das ¹

¹ Indian Statistical Institute, Kolkata, Stat-Math Unit, 203 BT Road, Kolkata, 700108, India

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     title = {Homotopy {\protect\emph{G}-algebra} structure on the cochain complex of hom-type algebras},
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Apurba Das. Homotopy G-algebra structure on the cochain complex of hom-type algebras. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1090-1099. doi : 10.1016/j.crma.2018.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.11.001/

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