## 146 Citations

Integrable quantum spin chains, non-skew symmetric r-matrices and quasigraded Lie algebras

- Mathematics
- 2006

On classical and quantum integrable field theories associated to Kac-Moody current algebras☆

- Mathematics, Physics
- 1991

A New Dynamical Reflection Algebra and Related Quantum Integrable Systems

- Mathematics, Physics
- 2012

We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang–Baxter equations, coactions, fusions,…

Construction of Dynamical Quadratic Algebras

- Mathematics
- 2003

We propose a dynamical extension of the quantum quadratic exchange algebras introduced by Freidel and Maillet. It admits two distinct fusion structures. A simple example is provided by the scalar…

New integrable Gaudin-type systems, classical r-matrices and quasigraded Lie algebras

- Mathematics
- 2005

Universal Construction of Algebras

- Mathematics
- 1998

Abstract:We present a direct construction of the abstract generators for q-deformed algebras. New quantum algebraic structures of type are thus obtained. This procedure hinges upon a twisted trace…

On quantum Freidel-Maillet algebra for non-ultralocal integrable systems

- Mathematics
- 2015

We consider the quantum algebra of transition matrices for non-ultralocal integrable systems, and show that a regularization of the singular operator products in the quantum algebra via Sklyanin’s…

Spin chains from dynamical quadratic algebras

- Mathematics, Physics
- 2005

We present a construction of integrable quantum spin chains where local spin–spin interactions are weighted by a ‘position’-dependent potential containing Abelian non-local spin dependence. This…

Quantum Group Symmetry of Integrable Systems With or Without Boundary

- Mathematics
- 2002

We present a construction of integrable hierarchies without or with boundary, starting from a single R-matrix, or equivalently from a ZF algebra. We give explicit expressions for the Hamiltonians and…

## References

SHOWING 1-10 OF 10 REFERENCES

Hamiltonian structures for integrable classical theories from graded Kac-Moody algebras

- Mathematics
- 1986

Central extensions of quantum current groups

- Mathematics
- 1990

We describe Hopf algebras which are central extensions of quantum current groups. For a special value of the central charge, we describe Casimir elements in these algebras. New types of generators…

Boundary conditions for integrable quantum systems

- Physics, Mathematics
- 1988

A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open…

QuantumR matrix for the generalized Toda system

- Mathematics
- 1986

We report the explicit form of the quantumR matrix in the fundamental representation for the generalized Toda system associated with non-exceptional affine Lie algebras.

Exactly solved models in statistical mechanics

- Physics
- 1982

exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical…