A cohomological characterization of Leibniz central extensions of Lie algebras

DOI10.1090/S0002-9939-07-08985-XzbMath1140.17003arXivmath/0605399WikidataQ123190380 ScholiaQ123190380MaRDI QIDQ5431648

Hu, Naihong, Dong Liu, Yufeng Pei

Publication date: 20 December 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605399

zbMATH Keywords

Kac-Moody algebrasLeibniz cohomologyinvariant symmetric bilinear formsLeibniz central extensions

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Lie algebras of vector fields and related (super) algebras (17B66) Infinite-dimensional Lie (super)algebras (17B65) Cohomology of Lie (super)algebras (17B56) Leibniz algebras (17A32)

Related Items (19)

Extensions of Leibniz superalgebras ⋮ Structure of the planar Galilean conformal algebra ⋮ Gröbner–Shirshov bases theory for Leibniz superalgebras ⋮ The global extension problem, co-flag and metabelian Leibniz algebras ⋮ Omni-Representations of Leibniz Algebras ⋮ Unified products for Leibniz algebras. Applications ⋮ Structures of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra ⋮ About Leibniz cohomology and deformations of Lie algebras ⋮ On Leibniz cohomology ⋮ On non-abelian extensions of Leibniz algebras ⋮ Extending structures for Lie algebras ⋮ Quantum Deformations of the Heisenberg-Virasoro Algebra ⋮ Leibniz central extension on centerless twisted Schrödinger-Virasoro algebra ⋮ Low-Dimensional Cohomology Groups of the Lie Algebras W(a,b) ⋮ Structure of the Extended Schrödinger–Virasoro Lie Algebra $\widetilde{\mathfrak{sv}}$ ⋮ Second Leibniz cohomology group of twisted \(N = 2\) superconformal algebra ⋮ The deformed Lie algebra of differential operators of order at most one ⋮ On a class of n-Leibniz deformations of the simple Filippov algebras ⋮ Leibniz central extensions of Lie superalgebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Moduli spaces of curves and representation theory
• Derivations and central extensions of finitely generated graded Lie algebras
• 2-cocycles on the algebra of differential operators
• On the low dimensional cohomology of some infinite dimensional simple Lie algebras
• Cohomology of tensor product quantum planes
• Leibniz cohomology for differentiable manifolds
• Some infinite-dimensional simple Lie algebras in characteristic \(0\) related to those of Block
• Universal enveloping algebras of Leibniz algebras and (co)homology
• On Leibniz homology
• Leibniz algebras associated with foliations.
• QUADRATIC LIE ALGEBRAS AND COMMUTATIVE ASSOCIATIVE ALGEBRAS
• Leibniz Central Extensions on Some Infinite-Dimensional Lie Algebras
• On Derivations of Lie Algebras
• Abelian extensions of leibniz algebras
• Central Extensions of Nonsymmetrizable Kac-Moody Algebras over Commutative Algebras
• A q-analog for the virasoro algebra
• The Second Leibniz Homology Group for Kac-Moody Lie Algebras
• Structure of Degenerate Block Algebras
• Homologie et cohomologie des algèbres de Lie

This page was built for publication: A cohomological characterization of Leibniz central extensions of Lie algebras