Special bi-invariant linear connections on Lie groups and finite dimensional Poisson structures

DOI10.1016/j.difgeo.2014.07.006zbMath1393.17037arXiv1312.2076OpenAlexW2012296767WikidataQ115356173 ScholiaQ115356173MaRDI QIDQ744139

Saïd Benayadi, Mohamed Boucetta

Publication date: 6 October 2014

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.2076

zbMATH Keywords

symplectic Lie algebraLie algebraLie groupPoisson algebrabi-invariant linear connectionsemi-symmetric linear connection

Mathematics Subject Classification ID

Poisson algebras (17B63) Connections (general theory) (53C05) Lie-admissible algebras (17D25)

Related Items (14)

A new approach to Leibniz bialgebras ⋮ Invariant bilinear forms on Leibniz superalgebras ⋮ Mini-workshop: Deformation quantization: between formal to strict. Abstracts from the mini-workshop held February 15--21, 2015. ⋮ Symplectic Novikov Lie algebras ⋮ Flat symplectic Lie algebras ⋮ Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras ⋮ ON REPRESENTATIONS OF SYMMETRIC LEIBNIZ ALGEBRAS ⋮ Unnamed Item ⋮ Leibniz Algebras with Invariant Bilinear Forms and Related Lie Algebras ⋮ Odd-quadratic Leibniz superalgebras ⋮ \(\frac12\)-derivations of Lie algebras and transposed Poisson algebras ⋮ Malcev–Poisson–Jordan algebras ⋮ Commutative post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras ⋮ Quadratic (resp. symmetric) Leibniz superalgebras

Cites Work

• Sur les transformations des variétés riemanniennes et kähleriennes
• Poisson algebras in terms of non-associative algebras
• Flexible Lie-admissible algebras
• A generalization of Bieberbach's theorem
• A noncommutative version of Lie algebras: Leibniz algebras
• Quantization of Poisson superalgebras and speciality of Jordan Poisson superalgebras
• Structure theorems on Riemannian spaces satisfying \(R(X,Y)\cdot R=0\). I: The local version
• Symplectic double extension of a symplectic Lie group
• Theory of connections
• Algebras with one operation including Poisson and other Lie-admissible algebras
• A Characterization of Invariant Affine Connections
• SYMPLECTIC CONNECTIONS
• Invariant Affine Connections on Homogeneous Spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Special bi-invariant linear connections on Lie groups and finite dimensional Poisson structures