Kuznetsova, A. Yu.; Patrin, Ye. V. On the structure of \(C^*\)-algebra generated by a family of partial isometries and multipliers. (English) Zbl 1345.46058 Armen. J. Math. 7, No. 1, 50-58 (2015). Summary: In the paper we consider an operator algebra generated by a family of partial isometries associated with a self-mapping on a countable set and by multipliers. An action of the unit circle on this algebra is specified that determines its \(\mathbb{Z}\)-grading. Under some conditions on the mapping the algebra is isomorphic to the crossed product of its fixed point subalgebra and the semigroup \(\mathbb{N}\). MSC: 46L55 Noncommutative dynamical systems Keywords:\(C^\ast \)-algebra; partial isometry; conditional expectation; Toeplitz algebra; crossed product; \(\ast\)-endomorphism PDFBibTeX XMLCite \textit{A. Yu. Kuznetsova} and \textit{Ye. V. Patrin}, Armen. J. Math. 7, No. 1, 50--58 (2015; Zbl 1345.46058) Full Text: Link