相关论文: Twist deformations for Yangians

We present a quantization of a Lie coideal structure for twisted half-loop algebras of finite-dimensional simple complex Lie algebras. We obtain algebra closure relations of twisted Yangians in Drinfeld J presentation for all symmetric…

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset…

We describe a unifying framework for the systematic construction of integrable deformations of integrable $\sigma$-models within the Hamiltonian formalism. It applies equally to both the `Yang-Baxter' type as well as `gauged WZW' type…

We consider a family of deformations of T^{1,1} in the Yang-Baxter sigma model approach. We first discuss a supercoset description of T^{1,1}, which makes manifest the full symmetry of the space and leads to the standard Sasaki-Einstein…

The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the $R$ matrix…

We introduce the notion of deformed quantum vertex algebra module associated with a braiding map. We construct two families of braiding maps over the Etingof-Kazhdan quantum vertex algebras associated with the rational $R$-matrices of…

A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…

Interesting deformations of AdS_5 x S^5 such as the gravity dual of noncommutative SYM and Sch\"odinger spacetimes have recently been shown to be integrable. We clarify questions regarding the reality and integrability properties of the…

It is known that Yang-Baxter sigma models provide a systematic way to study integrable deformations of both principal chiral models and symmetric coset sigma models. In the original proposal and its subsequent development, the deformations…

We present particularly simple new solutions to the Yang--Baxter equation arising from two--dimensional cyclic representations of quantum $SU(2)$. They are readily interpreted as scattering matrices of relativistic objects, and the quantum…

Yang-Baxter deformations of superstring sigma-models have recently inspired a supergravity solution generating technique. Using the open/closed string map and a Killing bi-vector as a deformation parameter, new solutions can be built, such…

We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasi-Yang-Baxter algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and…

Generalizing our recent joint paper with Vasily Pestun (arXiv:2001.04929), we construct a family of $SO(2r),Sp(2r),SO(2r+1)$ rational Lax matrices, polynomial in the spectral parameter, parametrized by the divisors on the projective line…

The theory of the set-theoretic Yang-Baxter equation is reviewed from a purely algebraic point of view. We recall certain algebraic structures called shelves, racks and quandles. These objects satisfy a self-distributivity condition and…

In this paper we investigate the algebraic geometric nature of a solution of the Yang-Baxter equation based on the quantum deformation of the centrally extended $sl(2|2)$ superalgebra proposed by Beisert and Koroteev \cite{BEKO}. We derive…

We combine the Yang-Baxter (YB) and bi-Yang-Baxter (bi-YB) deformations with higher-spin auxiliary field deformations to construct multi-parameter families of integrable deformations of the principal chiral model on a Lie group $G$ with…

We discuss quantum deformations of Jordanian type for Lie superalgebras. These deformations are described by twisting functions with support from Borel subalgebras and they are multiparameter in the general case. The total twists are…

Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start from the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the…

Twist deformation U_F(g) is equivalent to the quantum group Fun_d(G#) and has two preferred bases: the one originating from U(g) and that of the coordinate functions on the dual Lie group G#. The costructure of the Hopf algebra U_F(g) is…

Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local structure of the deformed geometries and the global…