Results 21 to 30 of about 16,880 (213)

The Lax pair for the fermionic Bazhanov-Stroganov R-operator

Physics Letters B, 2021
We derive the Lax connection of the free fermion model on a lattice starting from the fermionic formulation of Bazhanov-Stroganov's three-parameter elliptic parametrization for the R-operator.
A. Melikyan, G. Weber
doaj   +1 more source

Yang-Baxter Equations and Relative Rota-Baxter Operators for Left-Alia Algebras Associated to Invariant Theory

Journal of Nonlinear Mathematical Physics
Left-Alia algebras are a class of algebras with symmetric Jacobi identities. They contain several typical types of algebras as subclasses, and are closely related to the invariant theory.
Guilai Liu
exaly   +2 more sources

Multipermutation Solutions of the Yang–Baxter Equation [PDF]

Communications in Mathematical Physics, 2011
Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution consists of a set $X$ and a function r:X x X --> X x X which satisfies the braid relation. We examine solutions here mainly from the point of view of finite permutation groups: a solution gives rise to a map ...
Gateva-Ivanova, Tatiana, Cameron, Peter
openaire   +2 more sources

The tetrahedral Zamolodchikov algebra for the fermionic Bazhanov-Stroganov R-operator

Physics Letters B, 2020
We find the fermionic R-operator based on Bazhanov-Stroganov three-parameter elliptic parametrization of the free fermion model, and the corresponding Yang-Baxter and decorated Yang-Baxter equations, which are of the difference type in one of the ...
A. Melikyan
doaj   +1 more source

Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps

SciPost Physics, 2022
We consider one dimensional block cellular automata, where the local update rules are given by Yang-Baxter maps, which are set theoretical solutions of the Yang-Baxter equations.
Tamás Gombor, Balázs Pozsgay
doaj   +1 more source

Yang-Baxter maps and the discrete KP hierarchy [PDF]

, 2009
We present a systematic construction of the discrete KP hierarchy in terms of Sato–Wilson-type shift operators. Reductions of the equations in this hierarchy to 1+1-dimensional integrable lattice systems are considered, and the problems that arise with ...
Kakei, S., Willox, R., Nimmo, J.J.C.
core   +1 more source

Rota-Baxter operators on the polynomial algebras, integration and averaging operators [PDF]

, 2014
The concept of a Rota–Baxter operator is an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota–Baxter operators and integrals in the case of the polynomial algebra k[x] k[x] .
Guo, Li, Zheng, Shanghua, Rosenkranz, Markus, Markus Rosenkranz, Shanghua Zheng, Li Guo   +5 more
core   +1 more source

Optical simulation of the Yang-Baxter equation [PDF]

Physical Review A, 2008
15 pages, 7 figures; introduction and second section are dramatically rewritten, in order to improve the physical ...
Hu, Shuang-Wei, Hu, Ming-Guang, Xue, Kang, Ge, Mo-Lin   +3 more
openaire   +2 more sources

All Jordanian deformations of the $AdS_5 \times S^5$ superstring

SciPost Physics, 2023
We explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on $\mathfrak{psu}(2,2|4)$, corresponding to Jordanian Yang-Baxter deformations of the $AdS_5\times S^5$ superstring.
Riccardo Borsato, Sibylle Driezen
doaj   +1 more source

Yang-Baxter Equations

, 2006
Preprint of an Encyclopedia article (Encyclopedia of Mathematical Physics, eds. J.-P. Françoise, G.L. Naber and Tsou S.T., Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), volume 5, pages 465-473) extended with an appendix on relations of electric networks and solvable models. We welcome comments, especially on the added appendix. Please, note that the
Perk, Jacques H. H., Au-Yang, Helen
openaire   +3 more sources