Classification of U_q(sl_2)-module algebra structures on the quantum plane
Steven Duplij (Theory Group, Nuclear Physics Labs, V. N. Karazin, Kharkov National University, Ukraine), Sergey Sinel'shchikov (Mathematics, Division, B. I. Verkin Institute for Low Temperature Physics, Engineering,, Kharkov, Ukraine)
TL;DR
This paper classifies all Uq(sl2)-module algebra structures on the quantum plane, describing their isomorphism classes, composition series, and classical limits, providing a comprehensive understanding of these algebraic structures.
Contribution
It provides a complete classification of Uq(sl2)-module algebra structures on the quantum plane and analyzes their properties and classical limits.
Findings
List of all module algebra structures on the quantum plane
Description of uncountably many isomorphism classes
Computation of composition series and classical limits
Abstract
A complete list of Uq(sl2)-module algebra structures on the quantum plane is produced and the (uncountable family of) isomorphism classes of these structures are described. The composition series of representations in question are computed. The classical limits of the Uq(sl2)-module algebra structures are discussed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons