A compact presentation for the alternating central extension of the positive part of Uq(sl^2)

DOI10.26493/1855-3974.2669.58czbMath1502.17014arXiv2011.02463OpenAlexW3197894360MaRDI QIDQ5089703

Paul M. Terwilliger

Publication date: 15 July 2022

Published in: Ars Mathematica Contemporanea (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.02463

zbMATH Keywords

tridiagonal pair\(q\)-Serre relations\(q\)-Onsager algebra\(q\)-shuffle algebra

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) Combinatorial aspects of groups and algebras (05E16)

Related Items

A generating function associated with the alternating elements in the positive part of U_q(sl^2) ⋮ Using a q-shuffle algebra to describe the basic module V(Λ_0) for the quantized enveloping algebra Uq(sl^2) ⋮ The compact presentation for the alternating central extension of the \(q\)-Onsager algebra ⋮ Tridiagonal pairs, alternating elements, and distance-regular graphs ⋮ The \(q\)-Onsager algebra and its alternating central extension

Cites Work

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• Distance-regular graphs
• Bipartite \(Q\)-polynomial distance-regular graphs and uniform posets
• The attenuated space poset \(\mathcal{A}_q(N, M)\)
• An integrable structure related with tridiagonal algebras
• Deformed Dolan-Grady relations in quantum integrable models
• A new (in)finite-dimensional algebra for quantum integrable models
• A new current algebra and the reflection equation
• Distance-regular graphs and the \(q\)-tetrahedron algebra
• Quantum affine algebras
• Quantum groups and quantum shuffles
• A basis of type Poincaré-Birkhoff-Witt for the quantum algebra of \(\widehat{sl}(2)\)
• An action of the free product \(\mathbb{Z}_2 \star \mathbb{Z}_2 \star \mathbb{Z}_2\) on the \(q\)-Onsager algebra and its current algebra
• Braid group action for the \(q\)-Onsager algebra
• The alternating central extension for the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\)
• The alternating presentation of \(U_q(\widehat{gl_2})\) from Freidel-Maillet algebras
• The alternating central extension of the \(q\)-Onsager algebra
• The half-infinite XXZ chain in Onsager's approach
• Tridiagonal pairs of \(q\)-Racah type, the double lowering operator \({\psi}\), and the quantum algebra \(U_q(\mathfrak{sl}_2)\)
• TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS
• A deformed analogue of Onsager’s symmetry in the XXZ open spin chain
• The alternating PBW basis for the positive part of Uq(sl^2)
• Exact spectrum of the XXZ open spin chain from theq-Onsager algebra representation theory
• Introduction to quantum groups