Classification of U_q(sl_2)-module algebra structures on the quantum plane

B. I. Verkin Institute for Low Temperature Physics; Engineering; Kharkov; Nuclear Physics Labs; Sergey Sinel'shchikov (Mathematics Division; Steven Duplij (Theory Group; Ukraine); V. N. Karazin Kharkov National University

arxiv: 0905.1719 · v3 · pith:NHOV57XGnew · submitted 2009-05-12 · 🧮 math.QA · hep-th· math-ph· math.MP· math.RA· quant-ph

Classification of U_q(sl₂)-module algebra structures on the quantum plane

Steven Duplij (Theory Group , Nuclear Physics Labs , V. N. Karazin Kharkov National University , Ukraine) , Sergey Sinel'shchikov (Mathematics Division , B. I. Verkin Institute for Low Temperature Physics , Engineering , Kharkov This is my paper

classification 🧮 math.QA hep-thmath-phmath.MPmath.RAquant-ph

keywords structuresalgebramoduleplanequantumclassesclassicalclassification

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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 structures are discussed.

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Classification of U_q(sl₂)-module algebra structures on the quantum plane

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