Nets of graded $C^*$-algebras over partially ordered sets
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S. A. Grigoryan, E. V. Lipacheva and A. S. Sitdikov
Translated by: the authors - St. Petersburg Math. J. 30 (2019), 901-915
- DOI: https://doi.org/10.1090/spmj/1576
- Published electronically: September 16, 2019
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Abstract:
The paper deals with $C^*$-algebras generated by a net of Hilbert spaces over a partially ordered set. The family of those algebras constitutes a net of $C^*$-algebras over the same set. It is shown that every such algebra is graded by the first homotopy group of the partially ordered set. Inductive systems of $C^*$-algebras and their limits over maximal directed subsets are considered, as well as properties of morphisms for nets of Hilbert spaces and nets of $C^*$-algebras.References
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Bibliographic Information
- S. A. Grigoryan
- Affiliation: Kazan State Power Engineering University, 51 Krasnoselskaya st., 420066 Kazan, Russia
- Email: gsuren@inbox.ru
- E. V. Lipacheva
- Affiliation: Kazan State Power Engineering University, 51 Krasnoselskaya st., 420066 Kazan, Russia
- Email: elipacheva@gmail.com
- A. S. Sitdikov
- Affiliation: Kazan State Power Engineering University, 51 Krasnoselskaya st., 420066 Kazan, Russia
- Email: airat_vm@rambler.ru
- Received by editor(s): December 1, 2017
- Published electronically: September 16, 2019
- © Copyright 2019 American Mathematical Society
- Journal: St. Petersburg Math. J. 30 (2019), 901-915
- MSC (2010): Primary 47L30, 46M40; Secondary 47L90
- DOI: https://doi.org/10.1090/spmj/1576
- MathSciNet review: 3882538