Related papers: Two FRT bialgebroids and their relations
We study the Yang-Baxter equation for the $R$-matrices of the six-vertex model. We analyze the solutions and give new parametrizations of the Yang-Baxter equation. In particular, we find the maximal commutative families of parametrized…
This is a review on infinite non-abelian symmetries in two-dimensional field theories. We show how any integrable QFT enjoys the existence of infinitely many {\bf conserved} charges. These charges {\bf do not commute} between them and…
We establish a correspondence between the invariant subsets of a non-degenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside…
Reductions for systems of ODEs integrable via the standard factorization method (the Adler-Kostant-Symes scheme) or the generalized factorization method, developed by the authors earlier, are considered. Relationships between such…
A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.
An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the…
A transformation is obtained which completes the unification of quadrirational Yang-Baxter maps and known integrable multi-quadratic quad equations. By combining theory from these two classes of quad-graph models we find an extension of the…
We establish a bialgebra theory for averaging algebras, called averaging antisymmetric infinitesimal bialgebras by generalizing the study of antisymmetric infinitesimal bialgebras to the context of averaging algebras. They are characterized…
The main aim of this paper is to determine reflections to bijective and non-degenerate solutions of the Yang-Baxter equation, by exploring their connections with their derived solutions. This is motivated by a recent description of left…
The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative "distributive" laws were defined. In an effort to study these…
In this work we refine the method of [1] and obtain a novel kind of functional equation determining the partition function of the elliptic SOS model with domain wall boundaries. This functional relation is originated from the dynamical…
In this paper, we introduce the definition of multiplicative $\omega$-Lie bialgebra, which is equivalent to the Manin triples and matched pairs. We also study the $\omega$-Yang-Baxter equation and Yang-Baxter $\omega$-Lie bialgebra. The…
Conformal classical Yang-Baxter equation and $S$-equation naturally appear in the study of Lie conformal bialgebras and left-symmetric conformal bialgebras. In this paper, they are interpreted in terms of a kind of operators, namely,…
A general functional definition of the infinite dimensional quantum $R$-matrix satisfying the Yang-Baxter equation is given. A procedure for the extracting a finite dimensional $R$-matrix from the general definition is demonstrated in a…
We show how so-called Yang-Baxter (YB) deformations of sigma models, based on an R-matrix solving the classical Yang-Baxter equation (CYBE), give rise to marginal current-current deformations when applied to the Wess-Zumino-Witten (WZW)…
The rules for Yang-Baxter (YB) deformation for a generic Green-Schwarz string sigma model has been obtained recently. We show that the deformation can be described through the action of a coordinate dependent $O(d,d)$ matrix on the target…
We consider two new families of quantum vertex algebras which are associated with the type $A$ trigonometric $R$-matrix and elliptic $R$-matrix of the eight-vertex model. We show that their $\phi$-coordinated representation theory is…
Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation are discussed and many consequences are derived. In particular, for each positive integer $n$ a finite square-free…
We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a…
We present Yang-Baxter maps associated to elliptic curves. They are related to discrete versions of the Krichever-Novikov and the Landau-Lifshits equations. A lifting of scalar integrable quad-graph equations to two-field equations is also…