Mariano Suarez-Alvarez

The Hilton-Heckmann argument for the anti-commutativity of cup products

We present a simple extension of the classical Hilton-Eckmann argument classically used to prove that the endomorphism monoid of the unit object in a monoidal category is commutative. It allows us to recover in a uniform way well-known results on the graded-commutativity of cup products defined on the cohomology theories attached to various algebraic structures, as well as some more recent results.We present a simple extension of the classical Hilton-Eckmann argument which proves that the endomorphism monoid of the unit object in a monoidal category is commutative. It allows us to recover in a uniform way well-known results on the graded-commutativity of cup products defined on the cohomology theories attached to various algebraic structures, as well as some more recent results.

Automorphisms and isomorphisms of quantum generalized Weyl algebras

Abstract We classify up to isomorphism the quantum generalized Weyl algebras and determine their automorphism groups in all cases in a uniform way, including the case where the parameter q is a root of unity, thereby completing the results obtained by Bavula and Jordan (2001) [5] and Richard and Solotar (2006) [12] .

Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case

We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of ‘quantum’ type in all but a few exceptional cases. 2010 MSC: 16E40, 16E65, 16U80, 16W50, 16W70.

PBW-deformations and deformations à la Gerstenhaber of N-Koszul algebras

In this article we establish an explicit link between the classical theory of deformations \`a la Gerstenhaber -- and a fortiori with the Hochschild cohomology-- and (weak) PBW-deformations of homogeneous algebras. Our point of view is of cohomological nature. As a consequence, we recover a theorem by R. Berger and V. Ginzburg, which gives a precise condition for a filtered algebra to satisfy the so-called PBW property, under certain assumptions.

A little bit of extra functoriality for Ext and the computation of the Gerstenhaber bracket

Abstract We show that the action of the Lie algebra HH 1 ( A ) of outer derivations of an associative algebra A on the Hochschild cohomology HH • ( A ) of A given by the Gerstenhaber bracket can be computed in terms of an arbitrary projective resolution of A as an A-bimodule, without having recourse to comparison maps between the resolution and the bar resolution.

Twisted Kähler differential forms

Abstract In this paper we construct a twisted analog of the differential graded algebra of Kahler differential forms on a commutative algebra (provided by an endomorphism α ). This construction generalizes the work done in (Contemp. Math. 279 (2001) 177–193) for topological purposes. The main feature of this twisted analog is a braiding which is the substitute of the commutativity in the classical situation, in which α is the identity. We show also that the one dimensional difference calculus is a particular case of our construction.