Geodesic
Gerstenhaber-schack and Hochschild cohomologies of Hopf algebras
Documenta mathematica, Tome 21 (2016), pp. 955-986.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We show that the Gerstenhaber-Schack cohomology of a Hopf algebra determines its Hochschild cohomology, and in particular its Gerstenhaber-Schack cohomological dimension bounds its Hochschild cohomological dimension, with equality of the dimensions when the Hopf algebra is cosemisimple of Kac type. Together with some general considerations on free Yetter-Drinfeld modules over adjoint Hopf subalgebras and the monoidal invariance of Gerstenhaber-Schack cohomology, this is used to show that both Gerstenhaber-Schack and Hochschild cohomological dimensions of the coordinate algebra of the quantum permutation group are 3.
Classification : 16T05, 16E40, 16E10
Keywords: Hopf algebra, cohomology, cohomological dimension, Yetter-Drinfeld module 
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     author = {Bichon, Julien},
     title = {Gerstenhaber-schack and {Hochschild} cohomologies of {Hopf} algebras},
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Bichon, Julien. Gerstenhaber-schack and Hochschild cohomologies of Hopf algebras. Documenta mathematica, Tome 21 (2016), pp. 955-986. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a18/