Related papers: Solutions of the classical Yang-Baxter equation an…

We promote the open-closed string map, originally formulated by Seiberg \& Witten, to a solution generating prescription in generalized supergravity. The approach hinges on a knowledge of an antisymmetric bivector $\Theta$, built from…

It is shown, under rather general smoothness conditions on the gauge potential, which takes values in an arbitrary semi-simple compact Lie algebra ${\bf g}$, that if a (${\bf g}$-valued) solution to the gauge covariant Laplace equation…

For any positive integer $n$ and any Lie group $\mathfrak{G}$, given a definite symmetric bilinear form on $\mathbb{R}^n$ and an $\hbox{Ad}$-invariant scalar product on the Lie algebra of $\mathfrak{G}$, we construct a variational problem…

This work is devoted to the study of a class of Poisson-Lie groups endowed with left invariant metrics. The triples $(G,\pi,<,>)$ are considered, where $G$ is a simply connected Lie group, ?$\pi$ is a multiplicative Poisson tensor and $<,>$…

In this paper we study the problem of classification of indecomposable solutions of the Yang-Baxter equation. Using a scheme proposed by Bachiller, Ced\'o, and Jespers, and recent advances in the classification of braces we classify all…

This paper studies operator forms of the nonhomogeneous associative classical Yang-Baxter equation (nhacYBe), extending and generalizing such studies for the classical Yang-Baxter equation and associative Yang-Baxter equation that can be…

To the Yang-Baxter equation an additional relation can be added. This is the reflection equation which appears in various places, with or without spectral parameter. For example, in factorizable scattering on a half-line, integrable lattice…

We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang-Baxter equation and their q-analogues. After providing some universal results on quasi-bialgebras and admissible Drinfeld…

Extension of the braid relations to the multiple braided tensor product of algebras that can be used for quantization of nonultralocal models is presented. The Yang--Baxter--type consistency conditions as well as conditions for the…

We obtain inequivalent classical r-matrices of the $osp(1|2)$ Lie superalgebra as real solutions of the graded (modified) classical Yang-Baxter equation, in such a way that the corresponding automorphism transformation is employed. Then,…

Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations…

We consider extended covariant teleparallel $(f(T))$ gravity whose action is analytic in the torsion scalar and which is sourced by an $su(2)$ valued Yang-Mills field. Specifically, we search for regular solutions to the coupled $f(T)$…

Let G be a finite dimensional simple complex group equipped with the standard Poisson Lie group structure. We show that all G-homogeneous (holomorphic) Poisson structures on $G/H$, where $H \subset G$ is a Cartan subgroup, come from…

Starting from the problem of describing cohomological invariants of Poisson manifolds we prove in a sense a ``no-go'' result: the differential graded Lie algebra of de Rham forms on a smooth Poisson manifold is formal.

Superimposed D-branes have matrix-valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics…

We complete the classification of $4\times 4$ regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer…

It is shown that square free set theoretic involutive non-degenerate solutions of the Yang-Baxter equation whose associated permutation group (referred to as an involutive Yang-Baxter group) is abelian are retractable in the sense of…

We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras,…

We construct $2^n$-families of solutions of the Yang-Baxter equation from $n$-products of three-dimensional $R$ and $L$ operators satisfying the tetrahedron equation. They are identified with the quantum $R$ matrices for the Hopf algebras…

In this note we study `a la Baxter [1] the possible integrable manifolds of the asymmetric eight-vertex model. As expected they occur when the Boltzmann weights are either symmetric or satisfy the free-fermion condition but our analysis…