Geodesic
Generic symmetries of the Laurent extension of quantum plane
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015), pp. 333-358.

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A list of generic $U_q(\mathfrak{sl}_2)$-module algebra structures on the Laurent polynomial algebra over the quantum plane with uncountably many isomorphism classes is produced. Also, a complete list of these structures is presented in which the action of Cartan generator of $U_q(\mathfrak{sl}_2)$ is not reduced to multiplying $x$ and $y$ (the generators of quantum plane) by constants. 
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S. Sinel'shchikov. Generic symmetries of the Laurent extension of quantum plane. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015), pp. 333-358. http://geodesic.mathdoc.fr/item/JMAG_2015_11_a1/

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