Category of some subalgebras of the Toeplitz algebra
UDC 517.9 We consider structure analysis of subalgebras of the Toeplitz algebra, which are generated by inverse subsemigroups of bicyclic semigroup. A category of sets of natural numbers of length $k < m$ is constructed, and each set is matched by some $C^{\ast}$-algebra. The result is a...
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| Date: | 2021 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/191 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.9
We consider structure analysis of subalgebras of the Toeplitz algebra, which are generated by inverse subsemigroups of bicyclic semigroup. A category of sets of natural numbers of length $k < m$ is constructed, and each set is matched by some $C^{\ast}$-algebra. The result is a category of $C^{\ast}$ -algebras. The existence of a functor between these categories has been proved. In particular, we find the conditions, under which the category of $C^{\ast}$-algebras turns into a bundle of $C^{\ast}$ -algebras. |
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| DOI: | 10.37863/umzh.v73i12.191 |