Hochschild cohomology of poset algebras and Steenrod operations

Jerry Lodder

doi:10.1016/j.crma.2016.01.003

Homological algebra/Topology

Hochschild cohomology of poset algebras and Steenrod operations

Presented by: the Editorial Board

Jerry Lodder ¹

¹ Mathematical Sciences, Dept. 3MB, New Mexico State University, Las Cruces, NM 88003, USA

Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 339-343.

Abstract
Résumé

We show that the isomorphism from the Hochschild cohomology of a poset algebra A to the simplicial cohomology of the classifying space of the category associated with A maps Gerstenhaber's pre-Lie product to Steenrod's cup-one product. On cochains, this map becomes an isomorphism of differential graded homotopy commutative algebras.

On démontre que l'isomorphisme de la cohomologie de Hochschild d'une algèbre poset A à la cohomologie simpliciale du classifiant de la catégorie associé à A applique le produit pré-Lie de Gerstenhaber au produit cup-one de Steenrod. Sur les cochaînes, cette application devient un isomorphisme des algèbres différentielles graduées commutatives à homotopie près.

Received: 2015-08-14
Accepted: 2016-01-05
Published online: 2016-02-15

DOI: 10.1016/j.crma.2016.01.003

Author's affiliations:

Jerry Lodder ¹

¹ Mathematical Sciences, Dept. 3MB, New Mexico State University, Las Cruces, NM 88003, USA

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     title = {Hochschild cohomology of poset algebras and {Steenrod} operations},
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Jerry Lodder. Hochschild cohomology of poset algebras and Steenrod operations. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 339-343. doi : 10.1016/j.crma.2016.01.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.003/

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