## 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 α 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 α.

Original language | English |
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Pages (from-to) | 604-640 |

Number of pages | 37 |

Journal | Journal of Algebra |

Volume | 546 |

DOIs | |

Publication status | Published - 15 Mar 2020 |

## Keywords

- Cohomology
- Globalization
- Partial action