Simplicity of Partial Crossed Products

2013/06/23 by Alexandre Baraviera, Baraviera, Alexandre, Wagner Cortes +3
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA) #math.OA #math.RA

paper · pdf · doi:10.48550/arxiv.1306.5468

Submitted for publication in 06/04

arxiv created 2013/06/23 · arxiv updated 2013/06/25

Abstract

In this article, we consider a twisted partial action α of a group G on a ring R and it is associated partial crossed product R*_α^wG. We study necessary and sufficient conditions for the commutativity and simplicity of R*_α^wG. Let R=C(X) the algebra of continuous functions of a topological space X on the complex numbers and C(X)*_αG the partial skew group ring, where α is a partial action of a topological group G on C(X). We study some topological properties to obtain results on the algebra C(X). Also, we study the simplicity of C(X)*_αG using topological properties and the results about the simplicity of partial crossed product obtained for R*_α^wG.

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• Partial crossed products as equivalence relation algebras
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• Partial Crossed Product of a group G vs Crossed Product of S(G)
• The twisted partial group algebra and (co)homology of partial crossed products