Geodesic
The Laurent Extension of Quantum Plane: a Complete List of $U_q(\mathfrak{sl}_2)$-Symmetries
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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This work finishes a classification of $U_q(\mathfrak{sl}_2)$-symmetries on the Laurent extension $\mathbb{C}_q\big[x^{\pm 1},y^{\pm 1}\big]$ of the quantum plane. After reproducing the partial results of a previous paper of the author related to symmetries with non-trivial action of the Cartan generator(s) of $U_q(\mathfrak{sl}_2)$ and the generic symmetries, a complete collection of non-generic symmetries is presented. Together, these collections constitute a complete list of $U_q(\mathfrak{sl}_2)$-symmetries on $\mathbb{C}_q\big[x^{\pm 1},y^{\pm 1}\big]$.
Keywords: quantum universal enveloping algebra, Hopf algebra, quantum symmetry, weight.
Mots-clés : Laurent polynomial 
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     author = {Sergey Sinel'shchikov},
     title = {The {Laurent} {Extension} of {Quantum} {Plane:} a {Complete} {List} of $U_q(\mathfrak{sl}_2)${-Symmetries}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a37/}
}
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Sergey Sinel'shchikov. The Laurent Extension of Quantum Plane: a Complete List of $U_q(\mathfrak{sl}_2)$-Symmetries. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a37/

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