Algebra Associated with a Map Inducing an Inverse Semigroup
- 作者: Kuznetsova A.1
-
隶属关系:
- Kazan (Volga region) Federal University
- 期: 卷 40, 编号 8 (2019)
- 页面: 1102-1112
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205211
- DOI: https://doi.org/10.1134/S1995080219080158
- ID: 205211
如何引用文章
详细
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.
作者简介
A. Kuznetsova
Kazan (Volga region) Federal University
编辑信件的主要联系方式.
Email: alla.kuznetsova@gmail.com
俄罗斯联邦, Kazan, Tatarstan, 420008