U_q (sl_2)-Symmetries of the Quantum Disc: a Complete List

DOI10.15407/mag17.04.484zbMath1492.81067arXiv1911.08445OpenAlexW4200361769MaRDI QIDQ5087694

Sergey D. Sinelshchikov

Publication date: 1 July 2022

Published in: Zurnal matematiceskoj fiziki, analiza, geometrii (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.08445

zbMATH Keywords

Hopf algebrainvolutionweightquantum symmetryquantum universal enveloping algebraquantum discgrading jump

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) Universal enveloping (super)algebras (17B35) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Applications of Lie groups to the sciences; explicit representations (22E70) Universal enveloping algebras of Lie algebras (16S30) Hopf algebras and their applications (16T05) Jump processes on general state spaces (60J76)

Cites Work

• The Laurent extension of quantum plane: a complete list of \(U_q(\mathfrak{sl}_2)\)-symmetries
• The two-parameter quantum deformation of the unit disc
• Classification of U_q(sl_2)-module algebra structures on the quantum plane
• Covariant q-differential operators and unitary highest weight representations for Uqsun,n
• Derivations et automorphismes de quelques algebras quantiques
• Generic Symmetries of the Laurent Extension of Quantum Plane
• \(q\)-analogues of some bounded symmetric domains
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