The alternating PBW basis for the positive part of Uq(sl^2)

DOI10.1063/1.5091801zbMath1421.82012arXiv1902.00721OpenAlexW2963859947MaRDI QIDQ5228053

Paul M. Terwilliger

Publication date: 8 August 2019

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.00721

zbMATH Keywords

cubic \(q\)-Serre relationsPoincaré-Birkhoff-Witt basis (PBW)

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Applications of Lie (super)algebras to physics, etc. (17B81) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Irreversible thermodynamics, including Onsager-Machlup theory (82C35) Irreversible thermodynamics, including Onsager-Machlup theory (82B35) Serre spectral sequences (55T10)

Related Items (12)

A generating function associated with the alternating elements in the positive part of U_q(sl^2) ⋮ Using Catalan words and a \(q\)-shuffle algebra to describe the Beck PBW basis for the positive part of \(U_q( \widehat{\mathfrak{sl}}_2)\) ⋮ A compact presentation for the alternating central extension of the positive part of Uq(sl^2) ⋮ The alternating central extension for the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\) ⋮ 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 alternating presentation of \(U_q(\widehat{gl_2})\) from Freidel-Maillet algebras ⋮ The alternating central extension of the \(q\)-Onsager algebra ⋮ On the second realization for the positive part of \(U_q (\widehat{sl_2})\) of equitable type ⋮ The \(q\)-Onsager algebra and its alternating central extension ⋮ The alternating central extension of the Onsager Lie algebra

Cites Work

• Unnamed Item
• The \(q\)-Onsager algebra and the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\)
• 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
• Quantum affine algebras
• Quantum groups and quantum shuffles
• A basis of type Poincaré-Birkhoff-Witt for the quantum algebra of \(\widehat{sl}(2)\)
• Dual canonical bases, quantum shuffles and \(q\)-characters
• The Lusztig automorphism of the \(q\)-Onsager algebra
• Using Catalan words and a \(q\)-shuffle algebra to describe a PBW basis for the positive part of \(U_q(\widehat{\mathfrak{sl}}_2)\)
• The \(q\)-Onsager algebra and the universal Askey-Wilson algebra
• 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
• An infinite-dimensional \(\square_q\)-module obtained from the \(q\)-shuffle algebra for affine \(\mathfrak{sl}_2\)
• Braid group action for the \(q\)-Onsager algebra
• TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
• The central extension of the reflection equations and an analog of Miki’s formula
• Introduction to quantum groups

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