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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2016, Volume 158, Book 2, Pages 180–193 (Mi uzku1361)  

This article is cited in 2 scientific papers (total in 2 papers)

On the structure of $C^*$-algebras generated by representations of the elementary inverse semigroup

S. A. Grigoryan, E. V. Lipacheva

Kazan State Power Engineering University, Kazan, 420066 Russia

Abstract: The class of $C^*$-algebras generated by the elementary inverse semigroup and being deformations of the Toeplitz algebra has been introduced and studied. The properties of these algebras have been investigated. All their irreducible representations and automorphism groups have been described. These algebras have been proved to be $\mathbb Z$-graded $C^*$-algebras. For a certain class of algebras in the family under consideration the compact quantum semigroup structure has been constructed.

Keywords: $C^*$-algebra, Toeplitz algebra, irreducible representation, inverse semigroup, automorphism group, compact quantum semigroup.

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Bibliographic databases:
UDC: 512.667+517.5
Received: 11.01.2016

Citation: S. A. Grigoryan, E. V. Lipacheva, “On the structure of $C^*$-algebras generated by representations of the elementary inverse semigroup”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 158, no. 2, Kazan University, Kazan, 2016, 180–193

Citation in format AMSBIB
\Bibitem{GriLip16}
\by S.~A.~Grigoryan, E.~V.~Lipacheva
\paper On the structure of $C^*$-algebras generated by representations of the elementary inverse semigroup
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2016
\vol 158
\issue 2
\pages 180--193
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1361}
\elib{https://elibrary.ru/item.asp?id=26416797}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Lipacheva, “An example of a cosimple and co-commutative compact quantum semigroup”, Russian Math. (Iz. VUZ), 62:2 (2018), 62–68  mathnet  crossref  isi
    2. S. A. Grigoryan, E. V. Lipacheva, A. S. Sitdikov, “Nets of graded $C^*$-algebras over partially ordered sets”, St. Petersburg Math. J., 30:6 (2019), 901–915  mathnet  crossref  mathscinet  isi  elib
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