Category of some subalgebras of the Toeplitz algebra
DOI:
https://doi.org/10.37863/umzh.v73i12.191Keywords:
C ∗ -algebras, the Toeplitz algebra, category of tuples with integers, functor, net bundles of C ∗ -algebrasAbstract
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∗-algebra. The result is a category of C∗ -algebras. The existence of a functor between these categories has been proved. In particular, we find the conditions, under which the category of C∗-algebras turns into a bundle of C∗ -algebras.
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