Category of some subalgebras of the Toeplitz algebra

  • K. H. Hovsepyan Ijevan Branch of Yerevan State University
Keywords: C ∗ -algebras, the Toeplitz algebra, category of tuples with integers, functor, net bundles of C ∗ -algebras

Abstract

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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Published
17.12.2021
How to Cite
Hovsepyan, K. H. “Category of Some Subalgebras of the Toeplitz Algebra”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 12, Dec. 2021, pp. 1638 -46, doi:10.37863/umzh.v73i12.191.
Section
Research articles