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Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 10, Pages 89–93 (Mi ivm8105)  

This article is cited in 6 scientific papers (total in 6 papers)

Brief communications

A compact quantum semialgebra generated by an isometry

M. A. Aukhadiev, S. A. Grigoryan, E. V. Lipacheva

Chair of Higher Mathematics, Kazan State Energy University, Kazan, Russia

Abstract: In this paper we construct a compact quantum semigroup structure on a Toeplitz algebra. We prove the existence of a subalgebra in the dual algebra isomorphic to the algebra of regular Borel measures on a circle with the convolution product. We also prove the existence of a Haar functionals in the dual algebra and in the subalgebra mentioned above. We show that this compact quantum semigroup contains a dense subalgebra with the structure of a weak Hopf algebra.

Keywords: quantum semigroup, quantum group, Haar functional, Toeplitz algebra, weak Hopf algebra, inverse semigroup.

Full text: PDF file (161 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:10, 78–81

Bibliographic databases:

UDC: 512.667+517.5
Presented by the member of Editorial Board: Д. Х. Муштари
Received: 23.03.2011

Citation: M. A. Aukhadiev, S. A. Grigoryan, E. V. Lipacheva, “A compact quantum semialgebra generated by an isometry”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 10, 89–93; Russian Math. (Iz. VUZ), 55:10 (2011), 78–81

Citation in format AMSBIB
\Bibitem{AukGriLip11}
\by M.~A.~Aukhadiev, S.~A.~Grigoryan, E.~V.~Lipacheva
\paper A compact quantum semialgebra generated by an isometry
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 10
\pages 89--93
\mathnet{http://mi.mathnet.ru/ivm8105}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2918420}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 10
\pages 78--81
\crossref{https://doi.org/10.3103/S1066369X11100100}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84856246269}


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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. M. A. Aukhadiev, “Struktura nekotorykh kompaktnykh kvantovykh polugrupp”, Vladikavk. matem. zhurn., 15:2 (2013), 18–26  mathnet
    2. E. V. Lipacheva, K. G. Ovsepyan, “The structure of $C^*$-subalgebras of the Toeplitz algebra fixed with respect to a finite group of automorphisms”, Russian Math. (Iz. VUZ), 59:6 (2015), 10–17  mathnet  crossref
    3. Lipacheva E.V., Hovsepyan K.H., “the Structure of Invariant Ideals of Some Subalgebras of Toeplitz Algebra”, J. Contemp. Math. Anal.-Armen. Aca., 50:2 (2015), 70–79  crossref  mathscinet  zmath  isi
    4. E. V. Lipacheva, K. H. Hovsepyan, “Automorphisms of some subalgebras of the Toeplitz algebra”, Siberian Math. J., 57:3 (2016), 525–531  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. S. A. Grigoryan, E. V. Lipacheva, “O strukture $C^*$-algebr, porozhdennykh predstavleniyami elementarnoi inversnoi polugruppy”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 158, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2016, 180–193  mathnet  elib
    6. 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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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