Comptes Rendus
no. 4
Homological algebra/Topology
Hochschild cohomology of poset algebras and Steenrod operations
[La cohomologie de Hochschild des algèbres posets et les opérations de Steenrod]

Présenté par : the Editorial Board

Jerry Lodder1
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.

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.

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.

Reçu le :
Accepté le :
Publié le :
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 
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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/

[1] C. Berger; B. Fresse Combinatorial operad actions on cochains, Math. Proc. Camb. Philos. Soc., Volume 137 (2004) no. 1, pp. 135-174

[2] K. Costello Topological conformal field theories and Calabi–Yau categories, Adv. Math., Volume 210 (2007) no. 1, pp. 165-214

[3] M. Gerstenhaber The cohomology structure of an associative algebra, Ann. Math., Volume 78 (1962) no. 2, pp. 267-288

[4] M. Gerstenhaber; S. Schack Simplicial cohomology is Hochschild cohomology, J. Pure Appl. Algebra, Volume 30 (1983), pp. 143-156

[5] M. Gerstenhaber Self-dual and quasi self-dual algebras, Isr. J. Math., Volume 200 (2014), pp. 193-211

[6] M. Gerstenhaber; V. Voronov Homotopy G-algebras and moduli space operad, Int. Math. Res. Not., Volume 1995 (1995) no. 3, pp. 141-153

[7] V.A. Hinich; V.V. Schechtman On homotopy limit of homotopy algebras, K-Theory, Arithmetic and Geometry, Lecture Notes in Mathematics, vol. 1289, Springer Verlag, Heidelberg, 1987

[8] G. Hochschild On the cohomology groups of an associative algebra, Ann. Math., Volume 46 (1945) no. 1, pp. 58-67

[9] G. Hochschild On the cohomology theory for associative algebras, Ann. Math., Volume 47 (1946) no. 3, pp. 568-579

[10] M. Kontsevich; Y. Soibelman Notes on A∞-algebras, A∞-categories and non-commutative geometry, Homological Mirror Symmetry, Lecture Notes in Physics, vol. 757, Springer Verlag, Heidelberg, 2008

[11] N. Steenrod Products of cocycles and extensions of mappings, Ann. Math., Volume 48 (1947) no. 2, pp. 290-320

[12] T. Tradler; M. Zeinalian On the cyclic Deligne conjecture, J. Pure Appl. Algebra, Volume 204 (2006) no. 2, pp. 280-299

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