On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras

Abstract

We establish an improved upper estimate on dimension of any solvable algebra s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we consider Levi decomposable algebras with a given nilradical n and investigate restrictions on possible Levi factors originating from the structure of characteristic ideals of n. We present a new perspective on Turkowski's classification of Levi decomposable algebras up to dimension 9.

21 pages; major revision - one section added, another erased; author's version of the published paper

References in corpus (2)

• A class of solvable Lie algebras and their Casimir Invariants
• All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

Cited by in corpus (1)

• Lie structures and chain ideal lattices