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)


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.


Piecewise constant Crossed products Maximal commutative subalgebra 



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.


  1. 1.
    Carlsen, T.M., Silvestrov, S.D.: On the excel crossed product of topological covering maps. Acta Appl. Math. 108(3), 573–583 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Li, B.-R.: Introduction to Operator Algebras. World Scientific, Singapore - New Jersey - Hong Kong - London (1992)zbMATHGoogle Scholar
  3. 3.
    Öinert, J., Silvestrov, S.D.: Commutativity and ideals in algebraic crossed products. J. Gen. Lie Theory Appl. 2(4), 287–302 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Svensson, C., Silvestrov, S.D., de Jeu, M.: Dynamical systems and commutants in crossed products. Int. J. Math. 18, 455–471 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Svensson, C., Silvestrov, S.D., de Jeu, M.: Dynamical systems associated with crossed products. Acta Appl. Math. 108(3), 547–559 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Tomiyama, J.: Invitation to \(C^*-\)Algebras and Topological Dynamics. World Scientific, Singapore - New Jersey - Hong Kong - London (1987)CrossRefzbMATHGoogle Scholar

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

Personalised recommendations