Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane

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dc.contributor.authorDuplij, S.
dc.contributor.authorSinel’shchikov, S.
dc.date.accessioned2016-10-01T17:21:57Z
dc.date.available2016-10-01T17:21:57Z
dc.date.issued2010
dc.description.abstractA complete list of Uq(sl₂)-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 Uq(sl₂)-module algebra structures are discussed.uk_UA
dc.description.sponsorshipOne of the authors (S.D.) is thankful to Yu. Bespalov, J. Cuntz, B. Dragovich, J. Fuchs, A. Gavrilik, H. Grosse, D. Gurevich, J. Lukierski, M. Pavlov, H. Steinacker, Z. Rakic, W. Werner, and S. Woronowicz for fruitful discussions. Also he is grateful to the Alexander von Humboldt Foundation for valuable support as well as to J. Cuntz for kind hospitality at the Mathematisches Institut, Universit¨at M¨unster, where this paper was finalized. Both authors would like to express their gratitude to D. Shklyarov who attracted their attention to the fact that the results of this work were actually valid for q not being a root of unit, rather than for 0 < q < 1. We are also grateful to the referee who pointed out some inconsistencies in a previous version of the paper.uk_UA
dc.identifier.citationClassification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane / S. Duplij, S. Sinel’shchikov // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 4. — С. 406-430. — Бібліогр.: 13 назв. — англ.uk_UA
dc.identifier.issn1812-9471
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/106653
dc.language.isoenuk_UA
dc.publisherФізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН Україниuk_UA
dc.relation.ispartofЖурнал математической физики, анализа, геометрии
dc.statuspublished earlieruk_UA
dc.titleClassification of Uq(sl₂)-Module Algebra Structures on the Quantum Planeuk_UA
dc.typeArticleuk_UA

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Журнал математической физики, анализа, геометрии, 2010, № 4