The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra

DOI10.1016/J.JALGEBRA.2006.09.011zbMath1163.17026arXivmath-ph/0511004OpenAlexW2071756255MaRDI QIDQ876415

Brian Hartwig, Paul M. Terwilliger

Publication date: 18 April 2007

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

Full work available at URL: https://arxiv.org/abs/math-ph/0511004

zbMATH Keywords

Lie algebraloop algebraKac-Moody algebraOnsager algebra

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65)

Related Items (48)

Krichever–Novikov Type Algebras. A General Review and the Genus Zero Case ⋮ Finite-Dimensional Irreducible Modules for the Three-Point 2 Loop Algebra ⋮ An integral basis for the universal enveloping algebra of the Onsager algebra ⋮ Bidiagonal triads and the tetrahedron algebra ⋮ The tetrahedron algebra and its finite-dimensional irreducible modules ⋮ Finite-dimensional irreducible \(\square_q\)-modules and their Drinfel'd polynomials ⋮ Billiard arrays and finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules ⋮ On standard bases of irreducible modules of Terwilliger algebras of Doob schemes ⋮ The equitable presentation of \(\mathfrak{osp}_q(1|2)\) and a \(q\)-analog of the Bannai-Ito algebra ⋮ Unnamed Item ⋮ Generalized Onsager algebras ⋮ An LR pair that can be extended to an LR triple ⋮ The classification of Leonard triples of Racah type ⋮ The Terwilliger algebras of Johnson graphs ⋮ N-point Virasoro algebras are multipoint Krichever–Novikov-type algebras ⋮ Sharp tridiagonal pairs ⋮ Towards a classification of the tridiagonal pairs ⋮ The Leonard triples having classical type ⋮ Irreducible finite-dimensional representations of equivariant map algebras ⋮ An action of the tetrahedron algebra on the standard module for the Hamming graphs and Doob graphs ⋮ Tridiagonal pairs of Krawtchouk type ⋮ Leonard triples from the equitable basis of \(sl_2\) ⋮ Lowering-raising triples and \(U_q(\mathfrak{sl}_2)\) ⋮ Linear transformations that are tridiagonal with respect to the three decompositions for an LR triple ⋮ The structure of a tridiagonal pair ⋮ The switching element for a Leonard pair ⋮ Bidiagonal triples ⋮ Gröbner–Shirshov Basis for the Onsager and Tetrahedron Algebras ⋮ BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂) ⋮ The equitable basis for \({\mathfrak{sl}_2}\) ⋮ A classification of sharp tridiagonal pairs ⋮ Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules ⋮ Double lowering operators on polynomials ⋮ Finite dimensional modules for the \(q\)-tetrahedron algebra ⋮ Distance-regular graphs and the \(q\)-tetrahedron algebra ⋮ Classical Leonard pairs having LB-TD form ⋮ The universal enveloping algebra of sl2 and the Racah algebra ⋮ Distance-regular graphs of \(q\)-Racah type and the \(q\)-tetrahedron algebra ⋮ A tridiagonal linear map with respect to eigenbases of equitable basis ofsl₂ ⋮ Transition maps between the 24 bases for a Leonard pair ⋮ Tridiagonal pairs and the \(q\)-tetrahedron algebra ⋮ Linking the special orthogonal algebra \(\mathfrak{so}_4\) and the tetrahedron algebra \(\boxtimes \) ⋮ Defining relations for quantum symmetric pair coideals of Kac-Moody type ⋮ On the shape of a tridiagonal pair ⋮ The universal central extension of the three-point $\mathfrak {sl}_2$ loop algebra ⋮ Hypercube and tetrahedron algebra ⋮ A bidiagonal and tridiagonal linear map with respect to eigenbases of equitable basis ofsl₂ ⋮ The alternating central extension of the Onsager Lie algebra

Cites Work

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• Nonlinear holomorphic supersymmetry on Riemann surfaces
• Lie algebras with \(S_4\)-action and structurable algebras
• The chiral Potts models revisited.
• \(sl(N)\) Onsager's algebra and integrability
• Global geometric deformations of current algebras as Krichever-Novikov type algebras
• Three mutually adjacent Leonard pairs
• Chiral Potts model as a descendant of the six-vertex model
• ONSAGER ALGEBRA AND INTERGRABLE LATTICE MODELS
• TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
• Onsager’s algebra and the Dolan–Grady condition in the non-self-dual case
• Generalized Affine Kac-Moody Lie Algebras Over Localizations of the Polynomial Ring in One Variable
• Local cocycles and central extensions for multipoint algebras of Krichever-Novikov type
• Dolan–Grady relations and noncommutative quasi-exactly solvable systems
• The structure of quotients of the Onsager algebra by closed ideals *
• LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
• A Lie algebra for closed strings, spin chains, and gauge theories
• Universal central extensions of elliptic affine Lie algebras
• Four-Point Affine Lie Algebras
• ONSAGER'S ALGEBRA AND PARTIALLY ORTHOGONAL POLYNOMIALS
• Onsager's algebra and superintegrability
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other
• The \(sl_2\) loop algebra symmetry of the six-vertex model at roots of unity
• Nonlinear holomorphic supersymmetry, Dolan-Grady relations and Onsager algebra

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