Globalization of partial cohomology of groups

Dokuchaev, Mikhailo; Khrypchenko, Mykola; Simón, Juan

doi:10.1090/tran/8272

Globalization of partial cohomology of groups
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by Mikhailo Dokuchaev, Mykola Khrypchenko and Juan Jacobo Simón PDF

Trans. Amer. Math. Soc. 374 (2021), 1863-1898 Request permission

Abstract:

We study the relations between partial and global group cohomology with values in a commutative unital ring $\mathcal {A}$. In particular, for a unital partial action of a group $G$ on $\mathcal {A}$, such that $\mathcal {A}$ is a direct product of commutative indecomposable rings, we show that any partial $n$-cocycle of $G$ with values in $\mathcal {A}$ is globalizable.

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