Results 111 to 120 of about 44,436 (212)

Leibniz bialgebras, relative Rota-Baxter operators and the classical Leibniz Yang-Baxter equation

, 2020
In this paper, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras and Leibniz bialgebras are equivalent.
Sheng, Yunhe, Tang, Rong
core   +1 more source

Yang-Baxter deformations of the AdS4 × ℂℙ3 superstring sigma model

Journal of High Energy Physics, 2018
The gravity dual of β-deformed ABJM theory can be obtained by a TsT transformation of AdS4 × ℂℙ3. We present a supercoset construction of ℂℙ3 to obtain this gravity dual theory as a Yang-Baxter deformation.
René Negrón, Victor O. Rivelles
doaj   +1 more source

Commuting solutions of the Yang–Baxter matrix equation

Applied Mathematics Letters, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiu Ding, Chenhua Zhang, Noah H. Rhee
openaire   +2 more sources

On Some Unification Theorems: Yang–Baxter Systems; Johnson–Tzitzeica Theorem

Axioms
This paper investigates the properties of the Yang–Baxter equation, which was initially formulated in the field of theoretical physics and statistical mechanics.
Florin Felix Nichita
doaj   +1 more source

Tri-vector deformations in d = 11 supergravity

Journal of High Energy Physics, 2019
We construct a d = 11 supergravity analogue of the open-closed string map in the context of SL(5) Exceptional Field Theory (ExFT). The deformation parameter tri-vector Ω generalizes the non-commutativity bi-vector parameter Θ of the open string.
Ilya Bakhmatov, Nihat Sadik Deger, Edvard T. Musaev, Eoin Ó Colgáin, Mohammad M. Sheikh-Jabbari   +4 more
doaj   +1 more source

Diagonals of solutions of the Yang–Baxter equation

Forum Mathematicum
Abstract We study the diagonal mappings in non-involutive set-theoretic solutions of the Yang–Baxter equation. We show that, for non-degenerate solutions, they are commuting bijections. This gives the positive answer to the question: “Is every non-degenerate solution bijective?” of Cedó, Jespers and Verwimp.
Přemysl Jedlicka, Agata Pilitowska
openaire   +2 more sources

Statement B and the Yang-Baxter Equation

, 2011
This chapter reinterprets Statements A and B in a different context, and yet again directly proves that the reinterpreted Statement B implies the reinterpreted Statement A in Theorem 19.10.
Solomon Friedberg, Ben Brubaker, Daniel Bump   +2 more
core   +1 more source

Solutions of the Quantum Dynamical Yang-Baxter Equation and Dynamical Quantum Groups

, 1998
The quantum dynamical Yang-Baxter (QDYB) equation is a useful generalization of the quantum Yang-Baxter (QYB) equation. This generalization was introduced by Gervais, Neveu, and Felder. Unlike the QYB equation, the QDYB equation is not an algebraic but a
Etingof, Pavel, Varchenko, Alexander
core   +1 more source

Yang-Baxter deformations beyond coset spaces (a slick way to do TsT)

Journal of High Energy Physics, 2018
Yang-Baxter string sigma-models provide a systematic way to deform coset geometries, such as AdS p × S p , while retaining the σ-model integrability. It has been shown that the Yang-Baxter deformation in target space is simply an open-closed string map ...
I. Bakhmatov, E. Ó Colgáin, M. M. Sheikh-Jabbari, H. Yavartanoo   +3 more
doaj   +1 more source

Higher Conjugations and the Yang–Baxter Equation

Journal of Algebra, 2002
In a previous paper [Commun. Algebra 29, No. 8, 3351-3363 (2001; Zbl 0999.16034)] the author constructed actions of the symmetric groups on tensor powers of commutative or cocommutative Hopf algebras. The current paper sets these actions in the wider context of representations of the braid group and solutions of the Yang-Baxter equation, a ...
openaire   +1 more source