The amenability of the universal groupoids of a Clifford semigroup

Document Type : Original Article

Authors

Department of Mathematics, University of Qom, Qom, Iran

Abstract

We show that there is a one-to-one correspondence (up to isomorphism) between maximal subgroups of a Clifford semigroup and isotropy subgroups of its universal groupoid. We prove that a Clifford semigroup is a union of amenable subgroups if and only if its universal groupoid is amenable. We give an example of an amenable Clifford semigroup that its universal groupoid is not amenable.

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References

[1] Berglund, J.F., Junghenn, D., & Milnes, P. (1989). Analysis on Semigroups, Function Spaces. WileyInterscience and Canadian Mathematics Series of Monographs and Texts, Vol. 10, John Wiley, Sons.
[2] Day, M.M. (1957). Amenable semigroups. Illinois J. Math, 1, 509–544. DOI: https://doi.org/10.1215/ijm/1255380675.
[3] Exel, R., & Starling, C. Amenable actions of inverse semigroup. arXiv: 1411.2506v2 [math.OA]. DOI: https://doi.org/10.48550/arXiv.1411.2506.
[4] Lalone, S.M., & Milan, D. (2017). Amenability and uniqueness for groupoids associated with inverse semigroups. Semigroup Forum, 95, 321–344. DOI: https://doi.org/10.1007/s00233-016-9839-0.
[5] Paterson, L.T. (1999). Groupoids, Inverse Semigroups, and their Operator Algebras. Birkhaüser, NewYork. DOI: https://doi.org/10.1007/978-1-4612-1774-9.
[6] Renault, J. (1980). A groupoid approach to C∗-algebras. Lecture Notes in Mathematics, Vol. 793, Springer, Berlin. DOI: https://doi.org/10.1007/BFb0091072.
[7] Runde, V. (2002). Lectures on Amenability, Lecture Notes in Mathematics. Vol. 1774, Springer, Berlin. DOI: https://doi.org/10.1007/b82937.
[8] Sakai, K. (1994). On inner amenability of Clifford semigroups. Proc. Japan Acad, Ser. A Math. Sci, 70, 123–127. DOI: https://doi.org/10.3792/pjaa.70.123. 
Measure Algebras and Applications
Volume 1, Issue 1 - Serial Number 1
September 2023
Pages 107-118

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History

  • Receive Date: 28 May 2023
  • Revise Date: 24 August 2023
  • Accept Date: 26 August 2023

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