On symmetries of a quantum plane and its Laurent extension - Sinel’shchikov, S.D. (Reports of the National Academy of Sciences of Ukraine, 2014)
The structures of the Uq(sl2)-module algebra on the Laurent polynomial algebra over a quantum plane are considered. We establish a natural one-to-one correspondence between such structures and similar structures on the subalgebra of regular polynomials. A complete list of the above structures corresponding to the non-identity matrices from SL(2,Z) is presented.