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

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2010
• Main Authors: Duplij, S., Sinel’shchikov, S.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106653
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Classification 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.

A 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 structur...