A note on the algebra Uq(sl2)

DOI10.1080/00927872.2018.1530255zbMath1455.17016OpenAlexW2913880989MaRDI QIDQ5227797

Bo Hou, Li-hang Hou, Yali Song

Publication date: 7 August 2019

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2018.1530255

zbMATH Keywords

decompositioncenteridealquantum enveloping algebraequitable presentation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Cites Work

• The algebra \(U_q(\mathfrak{sl}_2)\) in disguise
• The universal Askey-Wilson algebra and the equitable presentation of \(U_{q}(sl_{2})\)
• \(p\)-inverting pairs of linear transformations and the \(q\)-tetrahedron algebra
• Distance-regular graphs and the \(q\)-tetrahedron algebra
• Distance-regular graphs of \(q\)-Racah type and the \(q\)-tetrahedron algebra
• The Lusztig automorphism of the \(q\)-Onsager algebra
• Dual polar graphs, the quantum algebra \(U_q(\mathfrak{sl}_{2})\), and Leonard systems of dual \(q\)-Krawtchouk type
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• Tridiagonal pairs of \(q\)-Racah type, the double lowering operator \({\psi}\), and the quantum algebra \(U_q(\mathfrak{sl}_2)\)
• The quantum algebra \(U_q(\mathfrak{sl}_2)\) and its equitable presentation
• Leonard pairs associated with the equitable generators of the quantum algebraU_q(sl₂)
• TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS
• Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules