On Uq (sl2)-actions on the Quantum Plane

S. Duplij, S. Sinel’shchikov


To give the complete list of Uq (sl2)-actions of the quantum plane, we first obtain the structure of quantum plane automorphisms. Then we introduce some special symbolic matrices to classify the series of actions using the weights. There are uncountably many isomorphism classes of the symmetries. We give the classical limit of the above actions.


quantum universal enveloping algebra; Hopf algebra; Verma module; representation; composition series; projection; weight

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague