A class of solvable Lie algebras and their Casimir Invariants
Abstract
A nilpotent Lie algebra nn,1 with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with nn,1 as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants of nn,1 and of its solvable extensions are calculated. For n=4 these algebras figure in the Petrov classification of Einstein spaces. For larger values of n they can be used in a more general classification of Riemannian manifolds.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.