Differential antisymmetric infinitesimal bialgebras, coherent derivations and Poisson bialgebras

DOI10.3842/sigma.2023.018zbMath1514.16028arXiv2207.00390MaRDI QIDQ6042954

Yuanchang Lin, X. Liu, Cheng-Ming Bai

Publication date: 4 May 2023

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.00390

zbMATH Keywords

differential algebraassociative Yang-Baxter equationdendriform algebraPoisson bialgebra\(\mathcal{O}\)-operatorantisymmetric infinitesimal bialgebra

Mathematics Subject Classification ID

Noncommutative geometry in quantum theory (81R60) Lie bialgebras; Lie coalgebras (17B62) Nonassociative algebras satisfying other identities (17A30) Bialgebras (16T10) Yang-Baxter equations (16T25)

Related Items (3)

Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebras ⋮ Differential mock-Lie bialgebras and admissible mock-Lie Yang-Baxter equations ⋮ Nijenhuis operators and associative D-bialgebras

Cites Work

• Unnamed Item
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• \(\mathcal O\)-operators on associative algebras and associative Yang-Baxter equations.
• \(n\)-Lie algebras
• Homological coalgebra
• On the structure of a differential algebra used by Connes and Lott
• Generalized derivations of Lie algebras
• Biderivations of the block Lie algebras
• Differential algebras in non-commutative geometry
• Hamilton formalism in non-commutative geometry
• Yang-Mills-Higgs versus Connes-Lott
• Double constructions of Frobenius algebras, Connes cocycles and their duality
• New generalized simple Lie algebras of Cartan type over a field with characteristic 0
• Coherent categorical structures for Lie bialgebras, Manin triples, classical \(r\)-matrices and pre-Lie algebras
• Noncommutative Poisson bialgebras
• The cohomology structure of an associative ring
• Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras
• On differential Rota-Baxter algebras.
• Generalized derivations of (color)n-ary algebras
• Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras
• Asymptotic Differential Algebra and Model Theory of Transseries
• $\mathcal{O}$-OPERATORS ON ASSOCIATIVE ALGEBRAS, ASSOCIATIVE YANG-BAXTER EQUATIONS AND DENDRIFORM ALGEBRAS
• On the operad of associative algebras with derivation
• Coalgebras and Bialgebras in Combinatorics
• Generalized Hamiltonian Dynamics
• CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.
• Splitting of Operations, Manin Products, and Rota–Baxter Operators
• Poisson bialgebras
• Operads of decorated trees and their duals
• Pre-Poisson algebras
• On the associative analog of Lie bialgebras

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