Algebra Associated with a Map Inducing an Inverse Semigroup
- Authors: Kuznetsova A.Y.1
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Affiliations:
- Kazan (Volga region) Federal University
- Issue: Vol 40, No 8 (2019)
- Pages: 1102-1112
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205211
- DOI: https://doi.org/10.1134/S1995080219080158
- ID: 205211
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Abstract
The algebra under study belongs to the class of operator algebras generated by a family of partial isometries, satisfying some relations on the initial and final projections. In turn, this family is uniquely determined by a self-mapping of a countable set. In the paper we consider a situation when isometry family generates an inverse semigroup. It is shown that in this (and only in this) case the corresponding C*-algebra has a nontrivial commutative AF-subalgebra, generated by a semi-lattice of projections of inverse semigroup. All invariant subspaces of the mentioned C*-algebra and its irreducible representations are described.
About the authors
A. Yu. Kuznetsova
Kazan (Volga region) Federal University
Author for correspondence.
Email: alla.kuznetsova@gmail.com
Russian Federation, Kazan, Tatarstan, 420008