Related papers: Stokes phenomenon and Yang-Baxter equations
We give an introduction to the "stable algebra of matrices" as related to certain problems in symbolic dynamics. We consider this stable algebra (especially, shift equivalence and strong shift equivalence) for matrices over general rings as…
We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of the classical braid groups. These representations naturally…
We construct and describe a family of groupoids over complex curves which serve as the universal domains of definition for solutions to linear ordinary differential equations with singularities. As a consequence, we obtain a direct,…
We generalize Nichita, Popovici and Tanasa solutions of the Braid equation to quasi-Yang-Baxter equation. We define quasi-braided Lie algebras in an additive monoidal category as a natural generalization of Majid's braided Lie algebra…
We derive a structure of $\mathbb{Z}[t,t^{-1}]$-module bundle from a family of Yang-Yang functions. For the fundamental representation of the complex simple Lie algebra of classical type, we give explicit wall-crossing formula and prove…
Skew bracoids have been shown to have applications in Hopf-Galois theory. We show that a certain family of skew bracoids correspond bijectively with left cancellative semibraces. A consequence of this correspondence is that skew bracoids in…
In analogy with non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation and braces, we define non-degenerate involutive partial set-theoretic solutions and partial braces. We define the structure group and the…
We study simple set-theoretic solutions of the Yang-Baxter equation that are finite and non-degenerate. Such retractable solutions are fully described and to investigate the irretracble solutions we give a new algebraic method. Our approach…
Involutive non-degenerate set theoretic solutions of the Yang-Baxter equation are considered, with a focus on finite solutions. A rich class of indecomposable and irretractable solutions is determined and necessary and sufficient conditions…
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are…
Let $V$ be a braided vector space, that is, a vector space together with a solution $\hat{R}\in {\text{End}}(V\otimes V)$ of the Yang--Baxter equation. Denote $T(V):=\bigoplus_k V^{\otimes k}$. We associate to $\hat{R}$ a solution…
We propose a dynamical matrix product ansatz describing the stochastic dynamics of two species of particles with excluded-volume interaction and the quantum mechanics of the associated quantum spin chains respectively. Analyzing consistency…
We investigate a family of (reducible) representations of Artin's braid groups corresponding to a specific solution to the Yang-Baxter equation. The images of the braid groups under these representations are finite groups, and we identify…
In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that…
We study the Stokes phenomenon for the solutions of the 1-dimensional complex heat equation and its generalizations with meromorphic initial data. We use the theory of Borel summability for the description of the Stokes lines, the…
We study categories whose objects are the braid representations, i.e. strict monoidal functors $F\colon B\rightarrow Mat$ from the braid category $B$ to the category of matrices $Mat$. Braid representations are equivalent to solutions to…
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations…
We construct two $Osp(n|2m)$ solutions of the graded Yang-Baxter equation by using the algebraic braid-monoid approach. The factorizable S-matrix interpretation of these solutions is also discussed.
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…
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…