2011/12/10 by David A. Towers, Towers, David A.
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.GR #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1112.2296
arxiv created 2013/05/07 · arxiv updated 2013/05/08
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 √(F) \not ⊆ F and L/R is a direct sum of isomorphic three-dimensional simple Lie algebras.