Related papers: A simple construction of elliptic $R$-matrices
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.
In this paper we study Leavitt path algebras over quivers with relations such as quantum Yang-Baxter equation, Hecke condition, and RTT conditions. This construction allows us to produce examples of Leavitt path algebras that contain…
The antisymmetric solution of the braided Yang--Baxter equation called the Bell matrix becomes interesting in quantum information theory because it can generate all Bell states from product states. In this paper, we study the quantum…
A connection between the Yang-Baxter relation for maps and the multi-dimensional consistency property of integrable equations on quad-graphs is investigated. The approach is based on the symmetry analysis of the corresponding equations. It…
In this paper we present representations of the recently introduced dilute Birman-Wenzl-Murakami algebra. These representations, labelled by the level-$l$ B$^{(1)}_n$, C$^{(1)}_n$ and D$^{(1)}_n$ affine Lie algebras, are Baxterized to yield…
We provide an explicit quantization of dynamical r-matrices for semisimple Lie algebras, classified earlier by the third author, which includes the Belavin-Drinfeld r-matrices. We do so by constructing an appropriate (dynamical) twist in…
Explicit solutions of the quantum Yang-Baxter equation are given corresponding to the non-unitary solutions of the classical Yang-Baxter equation for sl(5).
We construct $2^n+1$ solutions to the Yang-Baxter equation associated with the quantum affine algebras $U_q\big(A^{(1)}_{n-1}\big)$, $U_q\big(A^{(2)}_{2n}\big)$, $U_q\big(C^{(1)}_n\big)$ and $U_q\big(D^{(2)}_{n+1}\big)$. They act on the…
The Faddeev-Reshetikhin-Takhtajan method to construct matrix bialgebras from non-singular solutions of the quantum Yang-Baxter equation is extended to the anyonic or $\Z_n$-graded case. The resulting anyonic quantum matrices are braided…
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…
Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any…
By requiring invariance directly under the Yangian symmetry, we rederive Beisert's quantum R-matrix, in a form that carries explicit dependence on the representation labels, the braiding factors, and the spectral parameters u_i. In this…
The most common geometric interpretation of the Yang-Baxter equation is by braids, knots and relevant Reidemeister moves. So far, cubes were used for connections with the third Reidemeister move only. We will show that there are…
We obtain an R-matrix or matrix representation of the Artin braid group acting in a canonical way on the vector space of every (super)-Lie algebra or braided-Lie algebra. The same result applies for every (super)-Hopf algebra or…
We establish a one-to-one correspondence between a class of Garside groups admitting a certain presentation and the structure groups of non-degenerate, involutive and braided set-theoretical solutions of the quantum Yang-Baxter equation. We…
Solutions to the Yang-Baxter equation - an important equation in mathematics and physics - and their afforded braid group representations have applications in fields such as knot theory, statistical mechanics, and, most recently, quantum…
Modified universal R-matrices, associated with the central extension (through the Drinfeld's double construction) of the quantum groups U_q(sl_n), are realized through an infinite dimensional spectral parameter dependent solution for the…
A unified approach is applied in the consideration of the multi-parametric (colored) Yang-Baxter equations (YBE) and the usual YBE with two-parametric R-matrices, relying on the existence of the arbitrary functions in the general solutions.…
Quantum universal enveloping algebras, quantum elliptic algebras and double (deformed) Yangians provide fundamental algebraic structures relevant for many integrable systems. They are described in the FRT formalism by R-matrices which are…
Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang-Baxter solutions, also known as braid group generators. This was done for non-invertible braid operators in \cite{maity2025non}. In this work we extend…