The algebra \(U_q(\mathfrak{sl}_2)\) in disguise

DOI10.1016/j.laa.2014.07.022zbMath1348.17011arXiv1307.7572OpenAlexW2333189125MaRDI QIDQ401216

Sarah Bockting-Conrad, Paul M. Terwilliger

Publication date: 26 August 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.7572

zbMATH Keywords

quantum groupquantum enveloping algebraequitable presentationtridiagonal pair

Mathematics Subject Classification ID

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

Related Items

Tridiagonal pairs of q-Racah type, the Bockting operator ψ, and L-operators for U_q(L(sl_2)) ⋮ Tridiagonal pairs of \(q\)-Serre type and their linear perturbations ⋮ Compatibility and companions for Leonard pairs ⋮ Circular bidiagonal pairs ⋮ The Lusztig automorphism of Uq(𝔰𝔩2) from the equitable point of view ⋮ Twisting finite-dimensional modules for the \(q\)-Onsager algebra \(\mathcal{O}_q\) via the Lusztig automorphism ⋮ Unnamed Item ⋮ Near-bipartite Leonard pairs ⋮ Lowering-raising triples and \(U_q(\mathfrak{sl}_2)\) ⋮ Tridiagonal pairs of \(q\)-Racah-type and the \(q\)-tetrahedron algebra ⋮ Double lowering operators on polynomials ⋮ A note on the algebra Uq(sl2) ⋮ Freidel-Maillet type presentations of \(U_q(sl_2)\)

Cites Work

• Two commuting operators associated with a tridiagonal pair
• The universal Askey-Wilson algebra and the equitable presentation of \(U_{q}(sl_{2})\)
• The equitable basis for \({\mathfrak{sl}_2}\)
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• Dual polar graphs, the quantum algebra \(U_q(\mathfrak{sl}_{2})\), and Leonard systems of dual \(q\)-Krawtchouk type
• 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
• The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra
• Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view
• TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
• Leonard pairs associated with the equitable generators of the quantum algebraU_q(sl₂)
• THE AUGMENTED TRIDIAGONAL ALGEBRA
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