Related papers: Anticommutative extension of the Adler map

We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-Le-Zeilberger. The proofs are combinatorial and new even in the classical cases. We also give…

In this paper, by making use of category theory, we construct dynamical reflection maps, solutions to a version of the reflection equation associated with suitable dynamical Yang-Baxter maps, set-theoretic solutions to the braid relation…

In this letter we derive the Seiberg-Witten map for noncommutative super Yang-Mills theory in Wess-Zumino gauge. Following (and using results of) hep-th/0108045 we split the observer Lorentz transformations into a covariant particle Lorentz…

A noncommutative version of the (anti-) self-dual Yang-Mills equations is shown to be related via dimensional reductions to noncommutative formulations of the generalized (SO(3)/SO(2)) nonlinear Schrodinger (NS) equations, of the…

In this paper, I will show that, if a Lie algebra $\G$ acts on a manifold $P$, any solution of the classical Yang-Baxter equation on $\G$ gives arise to a Poisson tensor on $P$ and a torsion-free and flat contravariant connection (with…

We investigate some particular completely positive maps which admit a stable commutative Von Neumann subalgebra. The restriction of such maps to the stable algebra is then a Markov operator. In the first part of this article, we propose a…

According to Shibukawa, ternary systems defined on quasigroups and satisfying certain conditions provide a way of constructing dynamical Yang-Baxter maps. After noticing that these conditions can be interpreted as 3-dimensional…

Birational Yang-Baxter maps (`set-theoretical solutions of the Yang-Baxter equation') are considered. A birational map $(x,y)\mapsto(u,v)$ is called quadrirational, if its graph is also a graph of a birational map $(x,v)\mapsto(u,y)$. We…

We prove that one-dimensional elastic relativistic collisions satisfy the set-theoretical Yang-Baxter equation. The corresponding collision maps are symplectic and admit a Lax representation. Furthermore, they can be considered as…

In this paper, we first construct a graded Lie algebra which characterizes Rota-Baxter operators on an anti-flexible algebra as Maurer-Cartan elements. Next, we study infinitesimal deformations of bimodules over anti-flexible algebras. We…

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…

Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in…

For a large class of nonuniformly expanding maps of $\Bbb R^m$, with indifferent fixed points and unbounded distorsion and non necessarily Markovian, we construct an absolutely continuous invariant measure. We extend to our case techniques…

A family of nonparametric Yang Baxter (YB) maps is constructed by refactorization of the product of two 2 by 2 matrix polynomials of first degree. These maps are Poisson with respect to the Sklyanin bracket. For each Casimir function a…

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasi-classical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise…

Yang-Baxter (YB) map systems (or set-theoretic analoga of entwining YB structures) are presented. They admit zero curvature representations with spectral parameter depended Lax triples L1, L2, L3 derived from symplectic leaves of 2 x 2…

Yang--Baxter maps (YB maps) are set-theoretical solutions to the quantum Yang--Baxter equation. For a set $X=\Omega\times V$, where $V$ is a vector space and $\Omega$ is regarded as a space of parameters, a linear parametric YB map is a YB…

Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct definition of multipermutation solutions has not been…

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum…

We prove a substantial extension of an inverse spectral theorem of Ambarzumyan, and show that it can be applied to arbitrary compact Riemannian manifolds, compact quantum graphs and finite combinatorial graphs, subject to the imposition of…