On Semi-Modular Subalgebras of Lie Algebras Over Fields of Arbitrary Characteristic

Details On Semi-Modular Subalgebras of Lie Algebras Over Fields of Arbitrary Characteristic On Semi-Modular Subalgebras of Lie Algebras Over Fields of Arbitrary Characteristic

2008-04-09

arxiv.org/abs/0804.1468v3

Mathematics

Rings and Algebras

Scientific paper

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 Lie algebras over algebraically closed fields of characteristic p > 0 that have absolute toral rank less than or equal to 1 or are restricted, 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 perfect 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.

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