Related papers: Associative triples and Yang-Baxter equation

We classify trigonometric solutions to the associative Yang-Baxter equation (AYBE) for A = Mat_n, the associative algebra of n-by-n matrices. The AYBE was first presented in a 2000 article by Marcelo Aguiar and also independently by…

$A_3$-associative algebra is a generalization of associative algebra and is one of the four remarkable types of Lie-admissible algebras, along with associative algebra, left-symmetric algebra and right-symmetric algebra. This paper develops…

Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…

In this paper we propose versions of the associative Yang-Baxter equation and higher order $R$-matrix identities which can be applied to quantum dynamical $R$-matrices. As is known quantum non-dynamical $R$-matrices of Baxter-Belavin type…

We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have form of coupled ${\rm GL}(N)$ Sklyanin elliptic algebras. Then we…

We describe several methods of constructing R-matrices that are dependent upon many parameters, for example unitary R-matrices and R-matrices whose entries are functions. As an application, we construct examples of R-matrices with…

Yang-Baxter bialgebras, as previously introduced by the authors, are shown to arise from a double crossproduct construction applied to the bialgebra R T T = T T R, E T = T E R, \Delta(T) = T \hat{\otimes} T, \Delta(E) = E \hat{\otimes} T +…

In this paper, the different operator forms of classical Yang-Baxter equation are given in the tensor expression through a unified algebraic method. It is closely related to left-symmetric algebras which play an important role in many…

We construct spectral parameter dependent R-matrices for the quantized enveloping algebras of twisted affine Lie algebras. These give new solutions to the spectral parameter dependent quantum Yang-Baxter equation.

We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The study of a special case of anti-flexible…

We have constructed series of the spectral parameter dependent solutions to the Yang-Baxter equations defined on the tensor product of reducible representations with symmetry of quantum algebra. These series are produced as descendant…

We describe a geometric construction of all nondegenerate trigonometric solutions of the associative and classical Yang-Baxter equations. In the associative case the solutions come from symmetric spherical orders over the irreducible nodal…

Let $R$ be a Hecke solution to the Yang-Baxter equation and $K$ be a reflection equation matrix with coefficients in an associative algebra $\A$. Let $R(x)$ be the baxterization of $R$ and suppose that $K$ satisfies a polynomial equation…

The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines an R-matrix R(p), where $p$ stands for a set of mutually commuting variables. A family of SL(n)-type solutions of this equation provides a new realization of the…

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 twists of known solutions. We then focus on reflection and…

An explicit quantization is given of certain skew-symmetric solutions of the classical Yang-Baxter, yielding a family of $R$-matrices which generalize to higher dimensions the Jordanian $R$-matrices. Three different approaches to their…

We study Zamolodchikov algebras whose commutation relations are described by Belavin matrices defining a solution of the Yang-Baxter equation (Belavin $R$-matrices). Homomorphisms of Zamolodchikov algebras into dynamical algebras with…

We describe the construction of trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two irreducible representations of a quantum algebra $U_q(\G)$. Our method is a generalization of the tensor product…

This work addresses some relevant characteristics of associative algebras in low dimensions. Especially, given 1 and 2 dimensional associative algebras, we explicitly solve associative Yang-Baxter equations and use skew-symmetric solutions…

We examine links between the theory of braces and set theoretical solutions of the Yang-Baxter equation, and fundamental concepts from the theory of quantum integrable systems. More precisely, we make connections with Hecke algebras and we…