Pseudo-metric 2-step nilpotent Lie algebras
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Christian Autenried
und
Alexander Vasiľev
Abstract
The metric approach to studying 2-step nilpotent Lie algebras by making use of non-degenerate scalar products is realised. We show that a 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 the Lie bracket. This choice of the standard pseudo-metric form allows us 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 structure constants, which implies that the corresponding pseudo H-type groups admit lattices.
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© 2018 Walter de Gruyter GmbH Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Negative refraction and tiling billiards
- Classification of degree two curves in the symmetric square with positive self-intersection
- On lattice coverings by simplices
- On CMC hypersurfaces in 𝕊n+1 with constant Gauß–Kronecker curvature
- Fully truncated simplices and their monodromy groups
- Lie algebras of conservation laws of variational partial differential equations
- Feet in orthogonal-Buekenhout–Metz unitals
- Pseudo-metric 2-step nilpotent Lie algebras
Artikel in diesem Heft
- Frontmatter
- Negative refraction and tiling billiards
- Classification of degree two curves in the symmetric square with positive self-intersection
- On lattice coverings by simplices
- On CMC hypersurfaces in 𝕊n+1 with constant Gauß–Kronecker curvature
- Fully truncated simplices and their monodromy groups
- Lie algebras of conservation laws of variational partial differential equations
- Feet in orthogonal-Buekenhout–Metz unitals
- Pseudo-metric 2-step nilpotent Lie algebras
