Metric Lie algebras and quadratic extensions
By Ines Kath, M. Olbrich. 2003
52 citations recorded by the source corpus.
AbstractThe present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a nondegenerate invariant symmetric bilinear form. We show that any metric Lie algebra g without simple ideals has the structure of a so called balanced quadratic extension of an auxiliary Lie algebra l by an orthogonal l-module a in a canonical way. Identifying equivalence classes of quadratic extensions of l by a with a certain cohomology set H2Q(l,a), we obtain a classification scheme for general metric Lie algebras and a complete classification of metric Lie algebras of index 3.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/21380c6429f85c4994c0909ad26a759d65b0c830
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the structure of pseudo-Riemannian symmetric spaces (2004, background): “rlying metric Lie algebras which is also an isomorphism of Lie algebras with involution. 3 Quadratic cohomology of (l,θ l )-modules Let us first recall the notion of quadratic cohomology introduced in [KO2]. Let lbe a finite-dimensional Lie algebra. An orthogonal l-module is a tuple (ρ,a,h·,·i a) (als”