# 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} }

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

- 2000

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

- Mathematics
- 2002

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

- Mathematics
- 2013

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

- Mathematics
- 2012

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

- 2006

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

- Mathematics
- 2006

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

- MathematicsProceedings 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…

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ONSAGER ALGEBRA AND INTERGRABLE LATTICE MODELS

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