Hochschild cohomology of poset algebras and Steenrod operations

摘要

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. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.