Faithful representations of Lie algebras and Homogeneous Spaces

Abstract

The faithful representations of real Lie algebras g with dimensions $n\le 4$ acting on the dual space of the universal covering algebra of an ideal s of g, are calculated. With the help of left and right translations of the Lie group, we define the homogeneous manifolds of dimension n and we calculate the Killing fields (generators of left translations), the invariant fields (generators of right translations) and the left invariant 1-forms.

20 pages, no figures

References in corpus (6)

• The General Solution of Bianchi Type III Vacuum Cosmology
• 4+1 dimensional homogeneous anisotropic string cosmological models
• Lie algebra automorphisms as Lie point symmetries and the solution space for Bianchi Type I, II, IV, V vacuum geometries
• Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
• Quantizing preserving Noether symmetries
• On finite dimensional Lie algebras of planar vector fields with rational coefficients

Cited by in corpus (3)

• Noether analysis of Scalar-Tensor Cosmology
• Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
• The solution space to the Einstein's vacuum field equations for the case of five-dimensional Bianchi Type I (Type 4A1)