Algebraic Crossed Products by Partial Actions of Inverse Semigroups

Research Paper
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Abstract

In this work, for an inverse semigroup \(G\) and a partial action \(\pi\) on an algebra \({\text{A}},\) we define the crossed product \(A \times_{\pi }^{a} G\) as an enveloping \(C^{*}\)-algebra of a suitable \(*\)-algebra. At the end, we prove that the definition of crossed product we have presented here is equivalent to the one introduced in Tabatabaie Shourijeh and Moayeri Rahni (Crossed products by partial actions of inverse semigroups, 2015b).

Keywords

Inverse semigroup Partial action Universal inverse semigroup Covariant representation 

References

  1. Buss A, Exel R (2014) Inverse semigroup expansions and their actions on C*-algebras. J Illinois Math 56:1185–1212MathSciNetMATHGoogle Scholar
  2. Exel R, Vieira F (2010) Actions of inverse semigroups arising from partial actions of groups. J Math Anal Appl 363:86–96MathSciNetCrossRefMATHGoogle Scholar
  3. Tabatabaie Shourijeh B, Moayeri Rahni S (2015a) From the skew group ring to the skew inverse semigroup ring. arXiv:1504.04990v1 [math.OA] (under review)
  4. Tabatabaie Shourijeh B, Moayeri Rahni S (2015b) Crossed products by partial actions of inverse semigroups. arXiv:1504.05327v1 [math.OA] (under review)

Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesShiraz UniversityShirazIran

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