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Metric Lie algebras with maximal isotropic centre. (English) Zbl 1046.17003

The authors are interested in the classification of metric Lie algebras, that is, of finite-dimensional real Lie algebras equipped with an invariant non-degenerate symmetric bilinear form. In the present paper they determine the isomorphism classes of a certain type of solvable metric Lie algebras. They show that every metric Lie algebra of this type is a two-fold extension associated with an orthogonal representation of an abelian Lie algebra. The equivalence classes of such extensions are described by a certain cohomology set. As an application they obtain a classification scheme for metric Lie algebras with maximal isotropic center and the classification of metric Lie algebras of index 2.

MSC:

17B05 Structure theory for Lie algebras and superalgebras
53C35 Differential geometry of symmetric spaces
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