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Simplicity of Crossed Products by Twisted Partial Actions
In this article, we consider a twisted partial action α of a group G on an associative ring R and its associated partial crossed product R∗wαG. We provide necessary and sufficient conditions for the commutativity of R∗wαG when the twisted partial action α is unital. Moreover, we study necessary and sufficient conditions for the simplicity of R∗wαG in the following cases: (i) G is abelian; (ii) R is maximal commutative in R∗wαG; (iii) CR∗wαG(Z(R)) is simple; (iv) G is hypercentral. When R=C0(X) is the algebra of continuous functions defined on a locally compact and Hausdorff space X, with complex values that vanish at infinity, and C0(X)∗αG is the associated partial skew group ring of a partial action α of a topological group G on C0(X), we study the simplicity of C0(X)∗αG by using topological properties of X and the results about the simplicity of R∗wαG.
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