A class of solvable Lie algebras and their Casimir invariants. (English) Zbl 1063.22023

Šnobl, L.; Winternitz, P.

J. Phys. A, Math. Gen. 38, No. 12, 2687-2700 (2005).

Summary: A nilpotent Lie algebra \({\mathfrak n}_{n,1}\) with an \((n- 1)\)-dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with \({\mathfrak n}_{n,1}\) as their nilradical are obtained. Their dimension is at most \(n+ 2\). The generalized Casimir invariants of \({\mathfrak n}_{n,1}\) 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.

MSC:

17B30	Solvable, nilpotent (super)algebras
17B40	Automorphisms, derivations, other operators for Lie algebras and super algebras
17B70	Graded Lie (super)algebras
22E60	Lie algebras of Lie groups

Software:

CANONIK