On Levi extensions of nilpotent Lie algebras
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Universidad de La Rioja
info
ISSN: 0024-3795
Argitalpen urtea: 2013
Alea: 439
Zenbakia: 5
Orrialdeak: 1441-1457
Mota: Artikulua
Beste argitalpen batzuk: Linear Algebra and Its Applications
Lotura duten proiektuak
Laburpena
Levi's theorem decomposes any arbitrary Lie algebra over a field of characteristic zero, as a direct sum of a semisimple Lie algebra (named Levi factor) and its solvable radical. Given a solvable Lie algebra R, a semisimple Lie algebra S is said to be a Levi extension of R in case a Lie structure can be defined on the vector space S ⊕ R. The assertion is equivalent to ρ (S) ⊆ Der (R), where Der(R) is the derivation algebra of R, for some representation ρ of S onto R. Our goal in this paper, is to present some general structure results on nilpotent Lie algebras admitting Levi extensions based on free nilpotent Lie algebras and modules of semisimple Lie algebras. In low nilpotent index a complete classification will be given. The results are based on linear algebra methods and leads to computational algorithms. © 2013 Elsevier Inc. All rights reserved.