On the Lengths of Certain Chains of Subalgebras in Lie Algebras

Details On the Lengths of Certain Chains of Subalgebras in Lie Algebras On the Lengths of Certain Chains of Subalgebras in Lie Algebras

2011-12-10

arxiv.org/abs/1112.2296v1

Mathematics

Rings and Algebras

Scientific paper

In this paper we study the lengths of certain chains of subalgebras of a Lie algebra L: namely, a chief series, a maximal chain of minimal length, a chain of maximal length in which each subalgebra is modular in L, and a chain of maximal length in which each subalgebra is a quasi-ideal of L. In particular we show that, over a field of characteristic zero, a Lie algebra L with radical R has a maximal chain of subalgebras and a chain of subalgebras all of which are modular in L of the same length if and only if L = R or L/R is a direct sum of isomorphic three-dimensional non-split simple Lie algebras.

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