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Yang-Baxter deformations of WZW model on the Heisenberg Lie group
Nuclear Physics B, 2021 The Yang-Baxter (YB) deformations of Wess-Zumino-Witten (WZW) model on the Heisenberg Lie group (H4) are examined. We proceed to obtain the nonequivalent solutions of (modified) classical Yang-Baxter equation ((m)CYBE) for the h4 Lie algebra by using its
Ali Eghbali +2 more
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Majorana fermions solve the tetrahedron equations as well as higher simplex equations
Nuclear Physics BYang-Baxter equations define quantum integrable models. The tetrahedron and higher simplex equations are multi-dimensional generalizations. Finding the solutions of these equations is a formidable task.
Pramod Padmanabhan, Vladimir Korepin
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Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation
International Journal of Mathematics and Mathematical Sciences, 2000 This paper of tutorial nature gives some further details of proofs of some theorems related to the quantum dynamical Yang-Baxter equation. This mainly expands proofs given in Lectures on the dynamical Yang-Baxter equation by Etingof and Schiffmann ...
Tom H. Koornwinder
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Free integro-differential algebras and Groebner-Shirshov bases [PDF]
, 2014 The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such equations.
Guo, Li +5 more
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Yang-Baxter deformations of the AdS5 × S 5 pure spinor superstring
Journal of High Energy Physics, 2019 We present integrable Yang-Baxter deformations of the AdS5 × S 5 pure spinor superstring theory which were obtained by using homological perturbation theory. Its equations of motion and BRST symmetry are discussed and its Lax connection is derived.
Héctor A. Benítez, Victor O. Rivelles
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Generalized 11D supergravity equations from tri-vector deformations
European Physical Journal C: Particles and Fields, 2023 In Bakhmatov et al. (Phys. Rev. D 105(8): L081904, 2022) we presented a modification of 11-dimensional supergravity field equations which upon dimensional reduction yields generalized supergravity equations in 10-dimensions. In this paper we provide full
Ilya Bakhmatov +4 more
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Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations [PDF]
, 2009 We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution.
Gilson, C.R. +5 more
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Stokes Phenomenon and Yang–Baxter Equations [PDF]
Communications in Mathematical Physics, 2019 We describe the monodromy of dynamical Knizhnik-Zamolodchikov equations via Stokes phenomenon. It defines a family of braid groups representations by certain Stokes matrices. In particular, these Stokes matrices satisfy the Yang-Baxter equation.
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On a new class of non-dynamical ABCD algebras for classical and quantum integrable systems
Nuclear Physics BWe consider classical and quantum non-dynamical quadratic abcd Lax algebras with classical and quantum gl(n)⊗gl(n)-valued abcd-tensors satisfying a set of quadratic non-dynamical Yang-Baxter-type equations generalizing those of Fredel and Maillet [1]. We
T. Skrypnyk
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Semi-braces and the Yang–Baxter equation
Journal of Algebra, 2017 A brace is a set \(B\) together with two binary operations \(+\) and \(\circ\) such that \((B,+)\) is an abelian group, \((B,\circ)\) is a group, and \[ a\circ (b+c)= a\circ b - a +a \circ c, \] for all \(a,b,c\in B\). The importance of this algebraic structure is that a brace produces a set-theoretic solution of the Yang-Baxter equation, and, by ...
Catino, Francesco +2 more
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