# 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

- Mathematics
- 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 .

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…

-action on the Tetrahedron Algebra

- Mathematics
- 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
- 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…

Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories

- Mathematics
- 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…

## References

SHOWING 1-10 OF 42 REFERENCES

sl(N) Onsager's algebra and integrability

- Mathematics
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We define ansl(N) analog of Onsager's algebra through a finite set of relations that generalize the Dolan-Grady defining relations for the original Onsager's algebra. This infinite-dimensional Lie…

Onsager's algebra and superintegrability

- Mathematics
- 1990

The author considers the irreducible representations of the Onsager algebra, and shows that for a finite system, possessing such an algebra leads to an Ising-like structure in the spectra of…

KAC-Moody Lie Algebras and the Classification of Nilpotent Lie Algebras of Maximal Rank

- MathematicsCanadian Journal of Mathematics
- 1982

Introduction. The natural problem of determining all the Lie algebras of finite dimension was broken in two parts by Levi's theorem: 1) the classification of semi-simple Lie algebras (achieved by…

ONSAGER ALGEBRA AND INTERGRABLE LATTICE MODELS

- Mathematics
- 1991

We derive many integrable lattice from the Ising and superintegrable chiral Potts models using the Onsager algebra. For each of these models, we also construct a class of integrable models from the…

Onsager’s algebra and the Dolan–Grady condition in the non‐self‐dual case

- Mathematics
- 1991

In this paper, it is shown that a pair of operators that satisfy the Dolan–Grady conditions generate an Onsager algebra even in the case that they are not self‐dual. Briefly considered will be the…

Commuting transfer matrices in the chiral Potts models: Solutions of star-triangle equations with genus>1

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- 1987

Infinite-dimensional Lie algebras

- Mathematics
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1. Basic concepts.- 1. Preliminaries.- 2. Nilpotency and solubility.- 3. Subideals.- 4. Derivations.- 5. Classes and closure operations.- 6. Representations and modules.- 7. Chain conditions.- 8.…