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On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic.

Research output: Contribution to journalJournal article

Published

Journal publication date06/2008
JournalAsia-European Journal of Mathematics
Journal number2
Volume1
Number of pages12
Pages283-294
Original languageEnglish

Abstract

This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. It is shown that, in certain circumstances, including for all solvable algebras, for all restricted Lie algebras over algebraically closed fields of characteristic > 7, and for all Lie algebras having the one-and-a-half generation property, the conditions of modularity and semi-modularity are equivalent, but that the same is not true for all Lie algebras over a field of characteristic three. Semi-modular subalgebras of dimensions one and two are characterised over (perfect, in the case of two-dimensional subalgebras) fields of characteristic different from 2, 3.

Bibliographic note

Preprint of an article submitted for consideration in Asia-European Journal of Mathematics © 2008 [copyright World Scientific Publishing Company] [http://www.worldscinet.com/aejm/]