In this paper, we review the basic concepts regarding quantum integrability. Special
emphasis is given on the algebraic content of integrable models. The associated algebras …

Connections between set-theoretic Yang–Baxter and reflection equations and quantum
integrable systems are investigated. We show that set-theoretic R-matrices are expressed as …

The principles of the theory of quantum groups are reviewed from the point of view of the
possibility of using them for deformations of symmetries in physics models. The R-matrix …

One-boundary Temperley–Lieb algebras in the XXZ and loop models Page 1 Journal of
Statistical Mechanics: Theory and Experiment One-boundary Temperley–Lieb algebras in the …

We study a model of densely packed self-avoiding loops on the annulus, related to the
Temperley–Lieb algebra with an extra idempotent boundary generator. Four different …

We diagonalize the Hamiltonian of the Temperley–Lieb loop model with open boundaries
using a coordinate Bethe ansatz calculation. We find that in the ground-state sector of the …

A bstract We introduce new\({U} _ {\mathfrak {q}}{\mathfrak {sl}} _2\)-invariant boundary
conditions for the open XXZ spin chain. For generic values of\(\mathfrak {q}\) we couple the …

The spectra of integrable spin chains are shown to be independent of the ordering of their
spins. As an application we introduce defects (local spin inhomogeneities in homogenous …

We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the
general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie …

We present an'algebraic treatment'of the analytical Bethe ansatz. For this purpose, we
introduce abstract monodromy and transfer matrices which provide an algebraic framework …