The Laurent Extension of Quantum Plane: a Complete List of $U_q(\mathfrak{sl}_2)$-Symmetries

Symmetry Integrability and Geometry-Methods and Applications

article

Sergey Sinel'shchikov¹ 

[1] Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

关键词: quantum universal enveloping algebra;    Hopf algebra;    Laurent polynomial;    quantum symmetry;    weight;   

DOI  :  10.3842/SIGMA.2019.038

来源: National Academy of Science of Ukraine

【 摘 要 】

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 $\mathbb{C}_q\big[x^{\pm 1},y^{\pm 1}\big]$.

【 授权许可】

Unknown