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

Towers, David A. (2008) On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic. Asian-European Journal of Mathematics, 1 (2). pp. 283-294. ISSN 1793-5571

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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.

Item Type:
Journal Article
Journal or Publication Title:
Asian-European Journal of Mathematics
Additional Information:
Preprint of an article submitted for consideration in Asia-European Journal of Mathematics © 2008 [copyright World Scientific Publishing Company] [http://www.worldscinet.com/aejm/]
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
ID Code:
8069
Deposited By:
Deposited On:
07 Apr 2008 08:05
Refereed?:
Yes
Published?:
Published
Last Modified:
14 Aug 2020 01:02