Classical Yang-Baxter equation from β-supergravity
Sign Up to like & getrecommendations! Published in 2019 at "Journal of High Energy Physics"
DOI: 10.1007/jhep01(2019)140
Abstract: A bstractYang-Baxter deformations of superstring σ-models have recently inspired a supergravity solution generating technique. Using the open/closed string map and a Killing bi-vector as a deformation parameter, new solutions can be built, such that the… read more here.
Keywords: supergravity; baxter equation; classical yang; yang baxter ... See more keywords
Fusion Formulas and Fusion Procedure for the Yang-Baxter Equation
Sign Up to like & getrecommendations! Published in 2017 at "Algebras and Representation Theory"
DOI: 10.1007/s10468-017-9692-1
Abstract: We use the fusion formulas of the symmetric group and of the Hecke algebra to construct solutions of the Yang–Baxter equation on irreducible representations of ????????N$\mathfrak {gl}_{N}$, ????????N|M$\mathfrak {gl}_{N|M}$, Uq(????????N)$U_{q}(\mathfrak {gl}_{N})$ and Uq(????????N|M)$U_{q}(\mathfrak {gl}_{N|M})$. The… read more here.
Keywords: fusion formulas; baxter equation; fusion procedure; yang baxter ... See more keywords
Conformal classical Yang–Baxter equation, S-equation and $${\mathcal {O}}$$-operators
Sign Up to like & getrecommendations! Published in 2019 at "Letters in Mathematical Physics"
DOI: 10.1007/s11005-019-01243-2
Abstract: Conformal classical Yang–Baxter equation and S-equation naturally appear in the study of Lie conformal bialgebras and left-symmetric conformal bialgebras. In this paper, they are interpreted in terms of a kind of operators, namely $$\mathcal O$$-operators… read more here.
Keywords: baxter equation; conformal classical; classical yang; baxter ... See more keywords
On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Algebra"
DOI: 10.1080/00927872.2019.1710163
Abstract: Abstract We develop a method to construct all the indecomposable involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation with a prime-power number of elements and cyclic permutation group. Moreover, we give a complete classification of… read more here.
Keywords: solutions yang; baxter equation; theoretic solutions; indecomposable involutive ... See more keywords
Indecomposable solutions of the Yang-Baxter equation with permutation group of sizes pq and p2q
Sign Up to like & getrecommendations! Published in 2022 at "Communications in Algebra"
DOI: 10.1080/00927872.2023.2200827
Abstract: In this paper we study the problem of classification of indecomposable solutions of the Yang-Baxter equation. Using a scheme proposed by Bachiller, Ced\'o, and Jespers, and recent advances in the classification of braces we classify… read more here.
Keywords: solutions yang; indecomposable solutions; baxter equation; permutation ... See more keywords
Solutions of the Yang–Baxter equation for (n + 1) (2n + 1)-vertex models using a differential approach
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Statistical Mechanics: Theory and Experiment"
DOI: 10.1088/1742-5468/abf7be
Abstract: The formal derivatives of the Yang–Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the R matrix… read more here.
Keywords: baxter equation; differential approach; vertex models; yang baxter ... See more keywords
Decomposition Theorems for Involutive Solutions to the Yang–Baxter Equation
Sign Up to like & getrecommendations! Published in 2021 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnab232
Abstract: Motivated by the proof of Rump of a conjecture of Gateva–Ivanova on the decomposability of square-free solutions to the Yang–Baxter equation, we present several other decomposability theorems based on the cycle structure of a certain… read more here.
Keywords: decomposition theorems; solutions yang; baxter equation; yang baxter ... See more keywords
Anti-flexible bialgebras
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Algebra and Its Applications"
DOI: 10.1142/s0219498822502127
Abstract: We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The study of a special case… read more here.
Keywords: anti flexible; baxter equation; yang baxter; anti ... See more keywords
Set-theoretic solutions to the Yang–Baxter equation and generalized semi-braces
Sign Up to like & getrecommendations! Published in 2020 at "Forum Mathematicum"
DOI: 10.1515/forum-2020-0082
Abstract: Abstract This paper aims to introduce a construction technique of set-theoretic solutions of the Yang–Baxter equation, called strong semilattice of solutions. This technique, inspired by the strong semilattice of semigroups, allows one to obtain new… read more here.
Keywords: solutions yang; semi braces; baxter equation; theoretic solutions ... See more keywords
On Solutions to the Set-Theoretical Yang-Baxter Equation in Wajsberg-Algebras
Sign Up to like & getrecommendations! Published in 2018 at "Axioms"
DOI: 10.3390/axioms7010006
Abstract: In this work, we introduce Wajsberg algebras which are equivalent structures to MV-algebras in their implicational version, and then we define new notions and give new solutions to the set-theoretical Yang-Baxter equation by using Wajsberg… read more here.
Keywords: wajsberg algebras; set theoretical; baxter equation; solutions set ... See more keywords
Uniconnected solutions to the Yang–Baxter equation arising from self-maps of groups
Sign Up to like & getrecommendations! Published in 2021 at "Canadian Mathematical Bulletin"
DOI: 10.4153/s0008439521000230
Abstract: Abstract Set-theoretic solutions to the Yang–Baxter equation can be classified by their universal coverings and their fundamental groupoids. Extending previous results, universal coverings of irreducible involutive solutions are classified in the degenerate case. These solutions… read more here.
Keywords: baxter equation; equation arising; solutions yang; yang baxter ... See more keywords