Related papers: On the quantization of zero-weight super dynamical…
We derive the gravity duals of noncommutative gauge theories from the Yang-Baxter sigma model description of the AdS_5xS^5 superstring with classical r-matrices. The corresponding classical r-matrices are 1) solutions of the classical…
In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)), which is an abstract algebraic object leading to rational solutions of the Yang-Baxter equation on representations. We find that on the fundamental representation the…
We explain the concepts of computational statistical physics which have proven very helpful in the study of Yang-Mills integrals, an ubiquitous new class of matrix models. Issues treated are: Absolute convergence versus Monte Carlo…
Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each quantum superalgebra, belonging to the class of quasi-triangular Hopf superalgebras, contains a universal R-matrix…
We consider the modified (or twisted) Yang-Baxter equations for the $SL_{q}(N)$ groups and $SL_{q}(N|M)$ supergroups. The general solutions for these equations are presented in the case of the linear quantum (super)groups. The introduction…
We study right-invariant (resp., left-invariant) Poisson-Nijenhuis structures on a Lie group $G$ and introduce their infinitesimal counterpart, the so-called r-n structures on the corresponding Lie algebra $\mathfrak g$. We show that…
We provide explicit presentations of members of a suite of R matrices arising from the (\dot{0}_m|\alpha) representations of the quantum superalgebras U_q[gl(m|1)]. Our algorithm constructs both trigonometric and quantum R matrices; all of…
We argue that one can factorize the difference equation of hypergeometric type on the nonuniform lattices in general case. It is shown that in the most cases of q-linear spectrum of the eigenvalues this directly leads to the dynamical…
We construct lattice action for five-dimensional maximally supersymmetric Yang-Mills theory. This supersymmetric lattice formulation can be used to explore the non-perturbative regime of the continuum target theory, which has a known…
We construct a lattice action for ${\cal N}=4$ super Yang-Mills theory in four dimensions which is local, gauge invariant, free of spectrum doubling and possesses a single exact supersymmetry. Our construction starts from the observation…
The Perk--Schultz model may be expressed in terms of the solution of the Yang--Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra $U_q[sl(m|n)]$, with…
In this paper, we explain how generalized dynamical r-matrices can be obtained by (quasi-)Poisson reduction. New examples of Poisson structures and Poisson groupoid actions naturally appear in this setting. As an application, we use a…
A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying Uq(sl(2|1))…
In this paper we introduce a procedure that, given a solution to the Yang-Baxter equation as input, produces a stochastic (or Markovian) solution to (a possibly dynamical version of) the Yang-Baxter equation. We then apply this…
The classical and quantum dynamics of noncanonically coupled os- cillators is investigated in its relation to Lie superalgebras. It is shown that the quantum dynamics admits a hidden (super)hamiltonian formulation and, hence, preserves the…
Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ and its universal quantum $R$-matrix are explicitely constructed as functionals of the associated classical $r$-matrix. In this…
We investigate certain bases of Hecke algebras defined by means of the Yang-Baxter equation, which we call Yang-Baxter bases. These bases are essentially self-adjoint with respect to a canonical bilinear form. In the case of the degenerate…
Some examples are given of finite dimensional Lie bialgebras whose brackets and cobrackets are determined by pairs of $r$-matrices.
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…
Notions of an (H, X)-bialgebroid and of its dynamical representation are proposed. The dynamical representations of each (H, X)-bialgebroid form a tensor category. Every dynamical Yang-Baxter map R(lambda) satisfying suitable conditions, a…