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Crossed Product Algebras for Piece-Wise Constant Functions

  • Johan Richter
  • Sergei Silvestrov
  • Vincent Ssembatya
  • Alex Behakanira TumwesigyeEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 179)

Abstract

In this paper we consider algebras of functions that are constant on the sets of a partition. We describe the crossed product algebras of the mentioned algebras with \(\mathbb {Z}.\) We show that the function algebra is isomorphic to the algebra of all functions on some set. We also describe the commutant of the function algebra and finish by giving an example of piece-wise constant functions on a real line.

Keywords

Piecewise constant Crossed products Maximal commutative subalgebra 

Notes

Acknowledgements

This work was partially supported by the Swedish Sida Foundation - International Science Program. Alex Behakanira Tumwesigye thanks the Research environment MAM in Mathematics and Applied Mathematics, Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalens University for providing an excellent environment for research and education.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Johan Richter
    • 1
  • Sergei Silvestrov
    • 1
  • Vincent Ssembatya
    • 2
  • Alex Behakanira Tumwesigye
    • 2
    Email author
  1. 1.Division of Applied Mathematics, School of EducationCulture and Communication, Mälardalen UniversityVästeråsSweden
  2. 2.Department of Mathematics, College of Natural SciencesMakerere UniversityKampalaUganda

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