Related papers: Skein theoretic approach to Yang-Baxter homology
We perform an explicit two-loop calculation of the dilatation operator acting on single trace Wilson operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in N=2 and N=4 supersymmetric Yang-Mills…
We study the Yangian symmetry of the multicomponent Quantum Nonlinear Schrodinger hierarchy in the framework of the Quantum Inverse Scattering Method. We give an explicit realization of the Yangian generators in terms of the deformed…
Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier…
Quantum universal enveloping algebras, quantum elliptic algebras and double (deformed) Yangians provide fundamental algebraic structures relevant for many integrable systems. They are described in the FRT formalism by R-matrices which are…
We consider involutive, non-degenerate, finite set theoretic solutions of the Yang-Baxter equation. Such solutions can be always obtained using certain algebraic structures that generalize nil potent rings called braces. Our main aim here…
A Yang-Baxter relation-based formalism for generalized quantum affine algebras with the structure of an infinite Hopf family of (super-) algebras is proposed. The structure of the infinite Hopf family is given explicitly on the level of $L$…
The set-theoretical reflection equation and its solutions, the reflection maps, recently introduced by two of the authors, is presented in general and then applied in the context of quadrirational Yang-Baxter maps. We provide a method for…
We study a generalisation of the set-theoretic Yang-Baxter equation and investigate the connection between its solutions and matrix refactorisation problems. We refer to such solutions as scalene Yang-Baxter maps. Moreover, we construct…
Two "quantum enveloping algebras", here denoted by $U(R)$ and $U^{\sim}(R)$, are associated in [FRTa] and [FRTb] to any Yang-Baxter operator R. The latter is only a bialgebra, in general; the former is a Hopf algebra. In this paper, we…
The search for elliptic quantum groups leads to a modified quantum Yang-Baxter relation and to a special class of quasi-triangular quasi Hopf algebras. This paper calculates deformations of standard quantum groups (with or without spectral…
The Yang-Baxter equation for a $SU(2)\times U(1)$-symmetric $S=1/2$ spin-orbital chain was solved using the special computer algorithm developed by the author. The 8 new $R$-matrices separated on 5 groups are presented. Among the obtained…
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are…
We consider two approaches to isotopy invariants of oriented links: one from ribbon categories and the other from generalized Yang-Baxter operators with appropriate enhancements. The generalized Yang-Baxter operators we consider are…
We develop an approach for constructing the Baxter Q-operators for generic sl(N) spin chains. The key element of our approach is the possibility to represent a solution of the the Yang Baxter equation in the factorized form. We prove that…
In a previous work, we proposed an integrability setup for computing non-planar corrections to correlation functions in $\mathcal{N}=4$ super Yang-Mills theory at any value of the coupling constant. The procedure consists of drawing all…
A bootstrap program is presented for algebraically solving the $R$-matrix of a generic integrable quantum spin chain from its Hamiltonian. The Yang-Baxter equation contains an infinite number of seemingly independent constraints on the…
We suggest a cohomological framework to describe groups of $I$-type and involutive Yang-Baxter groups. These groups are key in the study of involutive non-degenerate set-theoretic solutions of the quantum Yang-Baxter equation. Our main tool…
The quantum Yang-Baxter equation is a braiding condition on vector spaces which is of high relevance in several fields of mathematics, such as knot theory and quantum group theory. Their combinatorial counterpart are set-theoretic solutions…
We find the general solution to the twisting equation in the tensor bialgebra $T({\bf R})$ of an associative unital ring ${\bf R}$ viewed as that of fundamental representation for a universal enveloping Lie algebra and its quantum…
Relative Rota-Baxter groups are generalisations of Rota-Baxter groups and introduced recently in the context of Lie groups. In this paper, we explore connections of relative Rota-Baxter groups with skew left braces, which are well-known to…