The non-toric \(U_q(sl_2)\)-symmetries on quantum polynomial algebra \(k_q[x^{\pm 1},y]\)

DOI10.1007/s41980-023-00832-1MaRDI QIDQ6185739

Li Bin Li, Xuejun Xia, Xiaoming Li

Publication date: 30 January 2024

Published in: Bulletin of the Iranian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

symmetryHopf algebraquantum polynomial algebranon-toric

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A quantum analogue of the first fundamental theorem of classical invariant theory
• Skew derivations and \(U_ q(sl(2))\)
• Quantum group actions, twisting elements, and deformations of algebras.
• Bialgebra actions, twists, and universal deformation formulas
• Pointed Hopf algebras acting on quantum polynomials
• The actions of quantum groups on quantum spaces.
• The Laurent extension of quantum plane: a complete list of \(U_q(\mathfrak{sl}_2)\)-symmetries
• Generalized derivations of a quantum plane.
• Automorphisms of the skew field of rational quantum functions
• Classification of U_q(sl_2)-module algebra structures on the quantum plane
• Actions of Pointed Hopf Algebras on Quantum Torus
• Derivations of skew polynomial rings