Andrea Solotar

Hochschild cohomology algebra of abelian groups

In this paper we present a direct proof of what is suggested by Holm’s results (T. Holm, The Hochschild cohomology ring of a modular group algebra: the commutative case, Comm. Algebra 24, 1957–1969 (1996)): there is an isomorphism of algebras HH*(kG,kG) → kG ⊗ H*(G,k) where G is a finite abelian group, k a ring, HH*(kG,kG) is the Hochschild cohomology algebra and H*(G,k) the usual cohomology algebra.This result agrees with the well-known additive structure result in force for any group G; we remark that the multiplicative structure result we have obtained is quite similar to the description of the monoidal category of Hopf bimodules over kG given in “C. Cibils, Tensor product of Hopf bimodules, to appear in Proc. Amer. Math. Soc”. This similarity leads to conjecture the structure of HH*(kG,kG) for G a finite group.

Isomorphisms between quantum generalized Weyl algebras

We study isomorphisms between generalized Weyl algebras, giving a complete answer to the quantum case of this problem for R = k[h].

Connected gradings and the fundamental group

The main purpose of this paper is to provide explicit computations of the fundamental group of several algebras. For this purpose, given a

Cohomology of split algebras and of trivial extensions

k

G-structure on the cohomology of Hopf algebras

-algebra

The Intrinsic Fundamental Group of a Linear Category

A

Hochschild and cyclic homology of Yang-Mills algebras

, we consider the category of all connected gradings of

N-complexes as functors, amplitude cohomology and fusion rules

A

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

by a group

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

G