Journal of Mathematical Physics, Analysis, Geometry
2021, vol. 17, No 4, pp. 484-508   https://doi.org/10.15407/mag17.04.484     ( to contents , go back )
https://doi.org/10.15407/mag17.04.484

Uq (sl2)-Symmetries of the Quantum Disc: a Complete List

Sergey D. Sinel'shchikov

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine

Received July 25, 2021.

Abstract

This work presents a classification of $U_q(\mathfrak{sl}_2)$-symmetries on the quantum disc. The principal invariant of such classification, the grading jump, is introduced. It turns out that, under the present subjects, the grading jump can take only 3 values: 0, 1, -1. The subcollection of the complete collection of symmetries is extracted in such a way that the selected symmetries satisfy certain compatibility condition for involutions.

Mathematics Subject Classification 2010: 81R50, 17B37
Key words: quantum universal enveloping algebra, Hopf algebra, quantum disc, quantum symmetry, grading jump, weight, involution

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