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

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On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic. / Towers, David A.
In: Asian-European Journal of Mathematics, Vol. 1, No. 2, 06.2008, p. 283-294.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Towers, DA 2008, 'On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic.', Asian-European Journal of Mathematics, vol. 1, no. 2, pp. 283-294. https://doi.org/10.1142/S1793557108000254

APA

Towers, D. A. (2008). On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic. Asian-European Journal of Mathematics, 1(2), 283-294. https://doi.org/10.1142/S1793557108000254

Vancouver

Towers DA. On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic. Asian-European Journal of Mathematics. 2008 Jun;1(2):283-294. doi: 10.1142/S1793557108000254

Author

Towers, David A. / On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic. In: Asian-European Journal of Mathematics. 2008 ; Vol. 1, No. 2. pp. 283-294.

Bibtex

@article{1c569b69ed484af68e878e036075169b,
title = "On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic.",
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.",
keywords = "Lie algebra, subalgebra lattice, modular, semi-modular",
author = "Towers, {David A.}",
note = "Preprint of an article submitted for consideration in Asia-European Journal of Mathematics {\textcopyright} 2008 [copyright World Scientific Publishing Company] [http://www.worldscinet.com/aejm/]",
year = "2008",
month = jun,
doi = "10.1142/S1793557108000254",
language = "English",
volume = "1",
pages = "283--294",
journal = "Asian-European Journal of Mathematics",
issn = "1793-5571",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",

}

RIS

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 -