A new approach to representations of 3-Lie algebras and abelian extensions

DOI10.1007/s10468-017-9693-0zbMath1430.17011arXiv1609.01549OpenAlexW2507154773MaRDI QIDQ1698225

Jiefeng Liu, Abdenacer Makhlouf, Yun He Sheng

Publication date: 15 February 2018

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01549

zbMATH Keywords

cohomologyrepresentationMaurer-Cartan elementabelian extension3-Lie algebrageneralized representation

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Cohomology of Lie (super)algebras (17B56) Other (n)-ary compositions ((n ge 3)) (17A42)

Related Items (10)

Abelian extensions of Lie triple systems with derivations ⋮ On 3-Lie algebras with a derivation ⋮ Symplectic, product and complex structures on 3-Lie algebras ⋮ On Non-Abelian Extensions of 3-Lie Algebras ⋮ Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras ⋮ Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and \(\mathcal{O}\)-operators ⋮ Generalized metricn-Leibniz algebras and generalized orthogonal representationof metric Lie algebras ⋮ Generalized derivation extensions of 3-Lie algebras and corresponding Nambu-Poisson structures ⋮ Cohomology, derivations and abelian extensions of 3-Lie algebras ⋮ On the isomorphism of non-abelian extensions of \(n\)-Lie algebras

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