Commutative 2-cocycles on Lie algebras

Abstract

On Lie algebras, we study commutative 2-cocycles, i.e., symmetric bilinear forms satisfying the usual cocycle equation. We note their relationship with antiderivations and compute them for some classes of Lie algebras, including finite-dimensional semisimple, current and Kac-Moody algebras.

v7: minor changes; added ancillary file with GAP code

References in corpus (4)

• On $\delta$-derivations of Lie algebras and superalgebras
• The second homology group of current Lie algebras
• Classical r-matrices and Novikov algebras
• Vanishing of trace forms in low characteristics

Cited by in corpus (10)

• On $\delta$-derivations of Lie algebras and superalgebras
• Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebras
• Hom-Lie structures on Kac-Moody algebras
• A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie-Poisson bialgebras
• Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras
• New splittings of operations of Poisson algebras and transposed Poisson algebras and related algebraic structures
• Anti-dendriform algebras, new splitting of operations and Novikov type algebras
• Deformations of Symmetric Simple Modular Lie (Super)Algebras
• Lie algebras and around: selected questions
• A new approach to the bialgebra theory for relative Poisson algebras