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Zh. Mat. Fiz. Anal. Geom., 2010, Volume 6, Number 4, Pages 406–430 (Mi jmag162)  

This article is cited in 1 scientific paper (total in 1 paper)

Classification of $U_q(\mathfrak{sl}_2)$-module algebra structures on the quantum plane

S. Duplija, S. D. Sinel'shchikovb

a Theory Group, Nuclear Physics Laboratory, V.N. Karazin Kharkiv National University, 4 Svoboda Sq., Kharkiv, 61077, Ukraine
b Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine

Abstract: A complete list of $U_q(\mathfrak{sl}_2)$-module algebra structures on the quantum plane is produced and the (uncountable family of) isomorphism classes of these structures are described. The composition series of representations in question are computed. The classical limits of the $U_q(\mathfrak{sl}_2)$-module algebra structures are discussed.

Key words and phrases: quantum universal enveloping algebra, Hopf algebra, Verma module, representation, composition series, weight.

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Document Type: Article
MSC: 33A15, 33B15, 33D05
Received: 02.01.2010

Citation: S. Duplij, S. D. Sinel'shchikov, “Classification of $U_q(\mathfrak{sl}_2)$-module algebra structures on the quantum plane”, Zh. Mat. Fiz. Anal. Geom., 6:4 (2010), 406–430

Citation in format AMSBIB
\Bibitem{DupSin10}
\by S.~Duplij, S.~D.~Sinel'shchikov
\paper Classification of $U_q(\mathfrak{sl}_2)$-module algebra structures on the quantum plane
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2010
\vol 6
\issue 4
\pages 406--430
\mathnet{http://mi.mathnet.ru/jmag162}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2789302}
\zmath{https://zbmath.org/?q=an:05897049}


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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. Duplij S., Hong Ya., Li F., “U-Q(Sl(M+1))-Module Algebra Structures on the Coordinate Algebra of a Quantum Vector Space”, J. Lie Theory, 25:2 (2015), 327–361  mathscinet  zmath  isi
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