Generalizations of the classical Yang-Baxter equation and ${\mathcal O}$O-operators

DOI10.1063/1.3600538zbMath1317.16031arXiv1302.0408OpenAlexW2038555916MaRDI QIDQ5266059

Xiang Ni, Li Guo, Cheng-Ming Bai

Publication date: 29 July 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.0408

zbMATH Keywords

quantum Yang-Baxter equationRota-Baxter operatorsLax pairs in integrable systems

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Exactly solvable models; Bethe ansatz (82B23) Applications of Lie algebras and superalgebras to integrable systems (17B80) Yang-Baxter equations (16T25)

Related Items (19)

Rota-Baxter operators on Witt and Virasoro algebras ⋮ Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras ⋮ Deformation of Kupershmidt operators and Kupershmidt-Nijenhuis structures of a Malcev algebra ⋮ Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation ⋮ On Hom-F-manifold algebras and quantization ⋮ Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras ⋮ Lagrangian and orthogonal splittings, quasitriangular Lie bialgebras, and almost complex product structures ⋮ Rota-Baxter 3-Lie algebras ⋮ Rota-Baxter operators on $\mathrm{sl(2,\mathbb {C})}$ sl (2,C) and solutions of the classical Yang-Baxter equation ⋮ Rota-Baxter operators and non-skew-symmetric solutions of the classical Yang-Baxter equation on quadratic Lie algebras ⋮ Rota-Baxter operators on 3-dimensional Lie algebras and the classical \(R\)-matrices ⋮ Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases ⋮ Free modified Rota-Baxter algebras and Hopf algebras ⋮ Rota-Baxter operators on pre-Lie superalgebras ⋮ Homogeneous averaging operators on simple finite conformal Lie algebras ⋮ Structure on the simple canonical Nambu Rota-Baxter 3-Lie algebra \(A_{\partial}\) ⋮ Deformations and cohomology theory of Rota-Baxter 3-Lie algebras of arbitrary weights ⋮ 3-BiHom-Lie superalgebras induced by BiHom-Lie superalgebras ⋮ Bihom-pre-Lie superalgebras and related structures

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• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
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