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Commutants in Crossed Product Algebras for Piecewise Constant Functions on the Real Line

  • Alex Behakanira TumwesigyeEmail author
  • Johan Richter
  • Sergei Silvestrov
Conference paper
  • 44 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 317)

Abstract

In this paper we consider commutants in crossed product algebras, for algebras of piece-wise constant functions on the real line acted on by the group of integers \(\mathbb {Z}\). The algebra of piece-wise constant functions does not separate points of the real line, and interplay of the action with separation properties of the points or subsets of the real line by the function algebra become essential for many properties of the crossed product algebras and their subalgebras. In this article, we deepen investigation of properties of this class of crossed product algebras and interplay with dynamics of the actions. We describe the commutants and changes in the commutants in the crossed products for the canonical generating commutative function subalgebras of the algebra of piece-wise constant functions with common jump points when arbitrary number of jump points are added or removed in general positions, that is when corresponding constant value set partitions of the real line change, and we give complete characterization of the set difference between commutants for the increasing sequence of subalgebras in crossed product algebras for algebras of functions that are constant on sets of a partition when partition is refined.

Keywords

Piece-wise constant functions Commutant Crossed product algebra Partition 

MSC 2010 Classification

16S35 16S36 16U70 

Notes

Acknowledgements

This research was supported by the Swedish International Development Cooperation Agency (Sida) and International Science Programme (ISP) in Mathematical Sciences (IPMS), Eastern Africa Universities Mathematics Programme (EAUMP). Alex Behakanira Tumwesigye is also grateful to the research environment Mathematics and Applied Mathematics (MAM), Division of Applied Mathematics, Mälardalen University for providing an excellent and inspiring environment for research education and research.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Alex Behakanira Tumwesigye
    • 1
    Email author
  • Johan Richter
    • 2
  • Sergei Silvestrov
    • 3
  1. 1.Department of MathematicsCollege of Natural Sciences, Makerere UniversityKampalaUganda
  2. 2.Department of Mathematics and Natural SciencesBlekinge Institute of TechnologyKarlskronaSweden
  3. 3.Division of Applied Mathematics, School of Education, Culture and CommunicationMälardalen UniversityVästeråsSweden

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