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Sbornik: Mathematics, 2014, Volume 205, Issue 3, Pages 319–342
DOI: https://doi.org/10.1070/SM2014v205n03ABEH004378 (Mi sm8199) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Operator approach to quantization of semigroups

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

Kazan State Power Engineering University
English version PDF (574 kB) Citations (12)
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DOI: https://doi.org/10.1070/SM2014v205n03ABEH004378
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
Received: 29.11.2012 and 10.12.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 3, Pages 15–40
DOI: https://doi.org/10.4213/sm8199
Bibliographic databases:
Document Type: Article
UDC: 517.98+512.667.7+517.98:530.145.6
MSC: Primary 46L05; Secondary 16T20, 46L65
Language: English
Original paper language: Russian
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://www.mathnet.ru/eng/sm/v205/i3/p15
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:568
    Russian version PDF:193
    English version PDF:12
    References:75
    First page:48
     
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