Quadratic algebras and integrable systems

  title={Quadratic algebras and integrable systems},
  author={Laurent Freidel and J. M. Maillet},
  journal={Physics Letters B},
A New Dynamical Reflection Algebra and Related Quantum Integrable Systems
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
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
Universal Construction of Algebras
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
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
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
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


Lax equations and quantum groups
Central extensions of quantum current groups
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
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
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
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