Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras

DOI10.1016/j.jalgebra.2023.06.006zbMath1530.17022arXiv2005.01110MaRDI QIDQ6114016

Yong Wu, Li Guo, Ruipu Bai, Cheng-Ming Bai

Publication date: 11 July 2023

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

Full work available at URL: https://arxiv.org/abs/2005.01110

zbMATH Keywords

Lie algebraNovikov algebraPoisson algebra\(n\)-Lie algebrapre-Lie algebra3-Lie algebratransposed Poisson algebra

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Poisson algebras (17B63) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36) Ternary compositions (17A40) Lie-admissible algebras (17D25) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Algebraic operads, cooperads, and Koszul duality (18M70)

Related Items (11)

Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebras ⋮ Transposed Poisson structures ⋮ Transposed Poisson structures on generalized Witt algebras and Block Lie algebras ⋮ Koszul duality, minimal model and \(L_\infty \)-structure for differential algebras with weight ⋮ Transposed Poisson structures on solvable and perfect Lie algebras ⋮ On the simple transposed Poisson algebras and Jordan superalgebras ⋮ Transposed Poisson structures on Lie incidence algebras ⋮ Transposed Poisson structures on the Lie algebra of upper triangular matrices ⋮ Transposed Poisson structures on Witt type algebras ⋮ Transposed Poisson structures on Galilean and solvable Lie algebras ⋮ Transposed Poisson structures on Block Lie algebras and superalgebras

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