We perform the structural analysis of C*-subalgebras of the Toeplitz algebra that are generated by inverse subsemigroups of a bicyclic semigroup. We construct a category of the sets of natural numbers of length k < m and associate each set with a certain C*-algebra. As a result, we obtain a category of C*-algebras. The existence of a functor between these categories is proved. In particular, we establish the conditions under which the category of C*-algebras turns into a bundle of C*-algebras.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 12, pp. 1638–1646, December, 2021. Ukrainian DOI: https://doi.org/10.37863/umzh.v73i12.191.
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Hovsepyan, K.H. Category of Some Subalgebras of the Toeplitz Algebra. Ukr Math J 73, 1895–1905 (2022). https://doi.org/10.1007/s11253-022-02036-y
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DOI: https://doi.org/10.1007/s11253-022-02036-y