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On the lengths of certain chains of subalgebras in Lie algebras

Towers, David (2014) On the lengths of certain chains of subalgebras in Lie algebras. Communications in Algebra, 42 (11). pp. 4778-4789. ISSN 0092-7872

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Abstract

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 F 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 ??? and L/R is a direct sum of isomorphic three-dimensional simple Lie algebras.

Item Type: Article
Journal or Publication Title: Communications in Algebra
Uncontrolled Keywords: Chief series ; Lie algebras ; Maximal chain ; Modular subalgebra ; Quasi\-ideal
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 69525
Deposited By: ep_importer_pure
Deposited On: 28 May 2014 13:10
Refereed?: Yes
Published?: Published
Last Modified: 23 Oct 2017 02:13
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/69525

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