Pseudo-metric 2-step nilpotent Lie algebras

2015/08/12 by Autenried, Christian, Furutani, Kenro, Markina, Irina +1 · 2 citations
#15A66 17B30 #22E25 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1508.02882

Abstract

The metric approach to studying 2-step nilpotent Lie algebras by making use of non-degenerate scalar products is realised. We show that any 2-step nilpotent Lie algebra is isomorphic to its standard pseudo-metric form, that is a 2-step nilpotent Lie algebra endowed with some standard non-degenerate scalar product compatible with Lie brackets. This choice of the standard pseudo-metric form allows to study the isomorphism properties. If the elements of the centre of the standard pseudo-metric form constitute a Lie triple system of the pseudo-orthogonal Lie algebra, then the original 2-step nilpotent Lie algebra admits integer structure constants. Among particular applications we prove that pseudo H-type algebras have bases with rational structural constants, which implies that the corresponding pseudo H-type groups admit lattices.

Cited by

• Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modules
• Stability analysis for the pseudo-Riemannian geodesic flows of step-two nilpotent Lie groups

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