TY - JOUR AU - K. H. Hovsepyan PY - 2021/12/17 Y2 - 2024/03/29 TI - Category of some subalgebras of the Toeplitz algebra JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 73 IS - 12 SE - Research articles DO - 10.37863/umzh.v73i12.191 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/191 AB - UDC 517.9We 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. ER -