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Mat. Sb., 2014, Volume 205, Number 3, Pages 15–40 (Mi msb8199)  

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

Operator approach to quantization of semigroups

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

Kazan State Power Engineering University

Abstract: The paper is devoted to the construction of compact quantum semigroups from semigroup $C^*$-algebras generated by the ‘deformation’ of algebras of continuous functions on compact Abelian groups. The dual space of such a $C^*$-algebra is endowed with the structure of a Banach *-algebra containing the algebra of measures on a compact group. We construct a weak Hopf *-algebra that is dense in such a compact quantum semigroup. We show that there exists an injective functor from the constructed category of compact quantum semigroups into the category of Abelian semigroups.
Bibliography: 25 titles.

Keywords: $C^*$-algebra, compact quantum semigroup, Haar functional, Toeplitz algebra, isometric representation.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-97016р-поволжье_а
14-01-31358мол_а

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8199

Full text: PDF file (632 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:3, 319–342

Bibliographic databases:

UDC: 517.98+512.667.7+517.98:530.145.6
MSC: Primary 46L05; Secondary 16T20, 46L65
Received: 29.11.2012 and 10.12.2013

Citation: M. A. Aukhadiev, S. A. Grigoryan, E. V. Lipacheva, “Operator approach to quantization of semigroups”, Mat. Sb., 205:3 (2014), 15–40; Sb. Math., 205:3 (2014), 319–342

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8199
  • http://mi.mathnet.ru/eng/msb/v205/i3/p15

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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. 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
    2. 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
    3. E. V. Lipacheva, “Ob odnom klasse graduirovannykh idealov polugruppovykh $C^*$-algebr”, Izv. vuzov. Matem., 2018, no. 10, 43–54  mathnet
    4. 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
    5. Lipacheva E.V., “Embedding Semigroup C-Algebras Into Inductive Limits”, Lobachevskii J. Math., 40:5, 1, SI (2019), 667–675  crossref  mathscinet  zmath  isi
    6. Grigoryan S.A., Gumerov R.N., Lipacheva E.V., “On Extensions of Semigroups and Their Applications to Toeplitz Algebras”, Lobachevskii J. Math., 40:12 (2019), 2052–2061  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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