Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic.
AU - Towers, David A.
N1 - Preprint of an article submitted for consideration in Asia-European Journal of Mathematics © 2008 [copyright World Scientific Publishing Company] [http://www.worldscinet.com/aejm/]
PY - 2008/6
Y1 - 2008/6
N2 - 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.
AB - 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.
KW - Lie algebra
KW - subalgebra lattice
KW - modular
KW - semi-modular
U2 - 10.1142/S1793557108000254
DO - 10.1142/S1793557108000254
M3 - Journal article
VL - 1
SP - 283
EP - 294
JO - Asian-European Journal of Mathematics
JF - Asian-European Journal of Mathematics
SN - 1793-5571
IS - 2
ER -