Twisting theory, relative Rota-Baxter type operators and \(L_\infty\)-algebras on Lie conformal algebras

DOI10.1016/j.jalgebra.2023.08.021arXiv2308.07596MaRDI QIDQ6054764

Jiefeng Liu, Lamei Yuan

Publication date: 25 October 2023

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2308.07596

zbMATH Keywords

cohomologytwistingLie conformal algebra\( L_\infty\)-algebratwisted relative Rota-Baxter operator

Mathematics Subject Classification ID

Homological methods in Lie (super)algebras (17B55) Nonassociative algebras satisfying other identities (17A30)

Cites Work

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• The variational Poisson cohomology
• Lie algebra structures on cohomology complexes of some \(H\)-pseudoalgebras
• Lie conformal algebra cohomology and the variational complex
• Derived brackets and sh Leibniz algebras
• From Poisson algebras to Gerstenhaber algebras
• An analytic problem whose solution follows from a simple algebraic identity
• What is a classical r-matrix?
• Quantization and dynamisation of trace-Poisson brackets
• Twisting on associative algebras and Rota-Baxter type operators.
• Quantum analogy of Poisson geometry, related dendriform algebras and Rota-Baxter operators
• Structure theory of finite conformal algebras
• Cohomology of conformal algebras
• Introduction to sh Lie algebras for physicists
• Splitting of operads and Rota-Baxter operators on operads
• Simple finite-dimensional double algebras
• Weak quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras
• Construction of Nijenhuis operators and dendriform trialgebras
• Quasi-Lie bialgebroids and twisted Poisson manifolds
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Conformal classical Yang-Baxter equation, \(S\)-equation and \({\mathcal{O}}\)-operators
• The Hopf algebras of signed permutations, of weak quasi-symmetric functions and of Malvenuto-Reutenauer
• Rota-Baxter operators on cocommutative Hopf algebras
• Integration and geometrization of Rota-Baxter Lie algebras
• Reynolds algebras and their free objects from bracketed words and rooted trees
• On antisymmetric infinitesimal conformal bialgebras
• Double Lie algebras of a nonzero weight
• Representations and cohomologies of relative Rota-Baxter Lie algebras and applications
• \(\mathcal{O}\)-operators and Nijenhuis operators of associative conformal algebras
• Poisson vertex algebras in the theory of Hamiltonian equations
• Left-symmetric conformal algebras and vertex algebras
• Lie theory for nilpotent \(L_{\infty}\)-algebras
• Deformations and their controlling cohomologies of \(\mathcal{O}\)-operators
• On conformal bialgebras
• On the structure of free Baxter algebras
• Some aspects of Baxter's functional equation
• Deformations and homotopy theory of relative Rota-Baxter Lie algebras
• What a Classical r-Matrix Really Is
• Strongly homotopy lie algebras
• Twisted Rota–Baxter operators and Reynolds operators on Lie algebras and NS-Lie algebras
• Splitting of Operations, Manin Products, and Rota–Baxter Operators
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• Baxter algebras and combinatorial identities. I
• Conformal r-matrix-Nijenhuis structures, symplectic-Nijenhuis structures, and ON-structures
• Theory of finite pseudoalgebras