| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 546, p. 604-640, MAR 15 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 15/09162-9 - Non commutative algebra and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |