2008/04/09 by David A. Towers, Towers, David A.
Mathematics · #17B05 #17B20 #17B30 #17B50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17B05 #msc:17B20 #msc:17B30 #msc:17B50
paper · pdf · doi:10.48550/arxiv.0804.1468
openalex publication_date 2008/04/09 · arxiv created 2008/06/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.