Let G be a finite subgroup of Sp(2n, C) acting by automorphisms in the Weyl algebra A n (C). We compute the Hochschild homology and cohomology groups of the invariant algebra A n (C) G. Ce texte est consacré au calcul de l'homologie et de la cohomologie de Hochschild des invariants de l'algèbre de Weyl A n = A n (C) sous l'action d'un sous-groupe fini G d'automorphismes contenu dans le groupe symplectique Sp(2n, C). Ce travail complète les calculs de [3], qui traitaient le cas du premier groupe d'homologie de Hochschild. Un exemple d'emploi de ce théorème est proposé en fin d'article.

In this work we study the class of algebras satisfying a duality property with respect to Hochschild homology and cohomology, as in [Proc. Amer. Math. Soc. 126 (1998) 1345-1348]. More precisely, we consider the class of algebras A such that there exists an invertible bimodule U and an integer number d with the property H • (A, M) ∼ = H d−• (A, U ⊗ A M), for all A-bimodules M. We show that this class is closed under localization and under smash products with respect to Hopf algebras satisfying also the duality property.We also illustrate the subtlety on dualities with smash products developing in detail the example S(V ) # G, the crossed product of the symmetric algebra on a vector space and a finite group acting linearly on V .  2004 Elsevier Inc. All rights reserved.

Research partially supported by UBACYT TW69 and CONICET. 2 Research member of CONICET (Argentina). * (gr(B), gr(B)). The only thing to be checked now is that the differential on the E 1 term can be identified to .df , and this is easily done.

Abstract. We prove that Ext•

For a given (X, S, β), where S, β : X × X → X × X are set theoretical solutions of Yang-Baxter equation with a compatibility condition, we define an invariant for virtual (or classical) knots/links using non commutative 2-cocycles pairs (f, g) that generalizes the one defined in [FG2]. We also define, a group U f g nc = U f g nc (X, S, β) and functions π f , π g : X × X → U f g nc (X) governing all 2-cocycles in X.We exhibit examples of computations achieved using [GAP2015].