The structure of quotients of the Onsager algebra by closed ideals *The structure of quotients of th

@article{Date1999TheSO,
title={The structure of quotients of the Onsager algebra by closed ideals *The structure of quotients of th},
author={Etsurō Date and Shi-Shyr Roan},
journal={Journal of Physics A},
year={1999}
}
• Published 3 November 1999
• Mathematics, Physics
• Journal of Physics A
We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through the use of formal Lie algebras.
54 Citations
THE ALGEBRAIC STRUCTURE OF THE ONSAGER ALGEBRA1
We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the
A Note on Quotients of the Onsager Algebra
We give another realization of the derived algebra of quotients of the Onsager algebra by an ideal corresponding to (t − 1) 2L .
Representations of twisted current algebras
We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop
The Onsager Algebra
In this thesis, four realizations of the Onsager algebra are explored. We begin with its original definition as introduced by Lars Onsager. We then examine how the Onsager algebra can be presented as
The Tetrahedron algebra, the Onsager algebra, and the sl2 loop algebra
• Mathematics
• 2007
Let K denote a field with characteristic 0 and let T denote an indeterminate. We give a presentation for the three-point loop algebra sl2⊗K[T,T−1,(T−1)−1] via generators and relations. This
-action on the Tetrahedron Algebra
The action of the symmetric group S4 on the Tetrahedron algebra, introduced by Hartwig and Terwilliger [HT05], is studied. This action gives a grading of the algebra which is related to its
A New Current Algebra and the Reflection Equation
• Mathematics, Physics
• 2010
We establish an explicit algebra isomorphism between the quantum reflection algebra for the \$\${U_q(\widehat{sl_2}) R}\$\$-matrix and a new type of current algebra. These two algebras are shown to be
The Tetrahedron algebra and its finite-dimensional irreducible modules
Abstract Recently Terwilliger and the present author found a presentation for the three-point sl 2 loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra ⊠ by
Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories
• Mathematics, Physics
• 2009
Generalizations of the q-Onsager algebra are introduced and studied. In one of the simplest case and q = 1, the algebra reduces to the one proposed by Uglov–Ivanov. In the general case and q ≠ 1, an
The \$S_4\$-action on tetrahedron algebra
• A. Elduque
• Mathematics
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
• 2007
The action of the symmetric group \$S_4\$ on the tetrahedron algebra, introduced by Hartwig and Terwilliger, is studied. This action gives a grading of the algebra which is related to its decomposition