Automorphisms of Real 4 Dimensional Lie Algebras and the Invariant Characterization of Homogeneous 4-Spaces

Abstract

The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the invariant characterization of the 4-dimensional homogeneous spaces which possess an invariant basis.

LaTeX2e, 23 pages, 2 Tables. To appear in Journal of Physics A: Mathematical & General

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Cited by in corpus (20)

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• The General Solution of Bianchi Type III Vacuum Cosmology
• Automorphisms and a Cartography of the Solution Space for Vacuum Bianchi Cosmologies: The Type III Case
• Automorphisms of real Lie algebras of dimension five or less
• Algebraic method for finding equivalence groups
• Complex and biHermitian structures on four dimensional real Lie algebras
• The General Solution of Bianchi Type $VI{I}_h$ Vacuum Cosmology
• Lie algebra automorphisms as Lie point symmetries and the solution space for Bianchi Type I, II, IV, V vacuum geometries
• Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D
• Invariant Poisson-Nijenhuis structures on Lie groups and classification
• Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality
• The solution space to the Einstein's vacuum field equations for the case of five-dimensional Bianchi Type I (Type 4A1)
• Faithful representations of Lie algebras and Homogeneous Spaces
• Automorphism group and ad-invariant metric on all six dimensional solvable real Lie algebras
• Some remarks on invariant Poisson quasi-Nijenhuis structures on Lie groups
• Surprising symmetry properties and exact solutions of Kolmogorov backward equations with power diffusivity
• A Non - Singular Cosmological Model with Shear and Rotation
• The signature of the Ricci curvature of left invariant Riemannian metrics on 4-dimensional Lie groups