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TMF, 1993, Volume 94, Number 2, Pages 193–199 (Mi tmf1416)  

This article is cited in 3 scientific papers (total in 4 papers)

Quantum groups, $q$ oscillators, and covariant algebras

P. P. Kulish

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: The physical interpretation of the basic concepts of the theory of covariant groups–coproducts, representations and corepresentations, action and coaction–is discussed for the examples of the simplest $q$ deformed objects (quantum groups and algebras, $q$ oscillators, and comodule algebras). It is shown that the reduction of the covariant algebra of quantum second-rank tensors includes the algebras of theq oscillator and quantum sphere. A special case of covariant algebra corresponds to the braid group in a space with nontrivial topology.

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English version:
Theoretical and Mathematical Physics, 1993, 94:2, 137–141

Bibliographic databases:

Received: 08.09.1992

Citation: P. P. Kulish, “Quantum groups, $q$ oscillators, and covariant algebras”, TMF, 94:2 (1993), 193–199; Theoret. and Math. Phys., 94:2 (1993), 137–141

Citation in format AMSBIB
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\by P.~P.~Kulish
\paper Quantum groups, $q$ oscillators, and covariant algebras
\jour TMF
\yr 1993
\vol 94
\issue 2
\pages 193--199
\mathnet{http://mi.mathnet.ru/tmf1416}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1221730}
\zmath{https://zbmath.org/?q=an:0973.17503}
\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 94
\issue 2
\pages 137--141
\crossref{https://doi.org/10.1007/BF01019325}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993LZ24300002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. V. Damaskinsky, P. P. Kulish, M. Chaichian, “Dynamic systems related to the Cremmer–Gervais $R$-matrix”, Theoret. and Math. Phys., 116:1 (1998), 820–828  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Baseilhac, P, “Deformed Dolan-Grady relations in quantum integrable models”, Nuclear Physics B, 709:3 (2005), 491  crossref  mathscinet  zmath  adsnasa  isi
    3. “Osnovnye nauchnye trudy Petra Petrovicha Kulisha”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 23, Zap. nauchn. sem. POMI, 433, POMI, SPb., 2015, 8–19  mathnet  mathscinet
    4. Kitanine N. Nepomechie R.I. Reshetikhin N., “Quantum Integrability and Quantum Groups: a Special Issue in Memory of Petr P Kulish”, J. Phys. A-Math. Theor., 51:11 (2018), 110201  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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