Category of some subalgebras of the Toeplitz algebra
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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