Comptes Rendus
no. 4
Homological algebra/Topology
Hochschild cohomology of poset algebras and Steenrod operations
the Editorial Board
Jerry Lodder1
1Mathematical Sciences, Dept. 3MB, New Mexico State University, Las Cruces, NM 88003, USA
Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 339-343

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.01.003

Jerry Lodder  1

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