Globalization of group cohomology in the sense of Alvares-Alves-Redondo

Autor(es)

Dokuchaev, Mikhailo ^[1] ; Khrypchenko, Mykola ^{[2, 3]} ; Jacobo Simon, Juan ^[4]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Fed Santa Catarina, Dept Matemat, Campus Reitor Joao David Ferreira Lima, BR-88040900 Florianopolis, SC - Brazil

^[3] Univ Nova Lisboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicacoes, P-2829516 Caparica - Portugal

^[4] Univ Murcia, Dept Matemat, E-30071 Murcia - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 546, p. 604-640, MAR 15 2020.
• Citações Web of Science: 0

Resumo

Recently E.R. Alvares, M.M. Alves and M.J. Redondo introduced a cohomology for a group G with values in a module over the partial group algebra K-par(G), which is different from the partial group cohomology defined earlier by the first two named authors of the present paper. Given a unital partial action alpha of G on a (unital) algebra A we consider A as a K-par(G)-module in a natural way and study the globalization problem for the cohomology in the sense of Alvares-Alves-Redondo with values in A. The problem is reduced to an extendibility property of cocycles. Furthermore, assuming that A is a product of blocks, we prove that any cocycle is globalizable, and globalizations of cohomologous cocycles are also cohomologous. As a consequence we obtain that the Alvares-Alves-Redondo cohomology group H-par(n)(G, A) is isomorphic to the usual cohomology group H-n(G, M(B)), where M(B) is the multiplier algebra of B and B is the algebra under the enveloping action of alpha. (C) 2019 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 15/09162-9 - Álgebra não comutativa e aplicações
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Temático