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Elementary Lie Algebras and Lie A-Algebras.

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Elementary Lie Algebras and Lie A-Algebras. / Towers, David A.; Varea, Vicente R.
In: Journal of Algebra, Vol. 312, No. 2, 15.06.2007, p. 891-901.

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

Harvard

Towers, DA & Varea, VR 2007, 'Elementary Lie Algebras and Lie A-Algebras.', Journal of Algebra, vol. 312, no. 2, pp. 891-901. https://doi.org/10.1016/j.jalgebra.2006.11.034

APA

Towers, D. A., & Varea, V. R. (2007). Elementary Lie Algebras and Lie A-Algebras. Journal of Algebra, 312(2), 891-901. https://doi.org/10.1016/j.jalgebra.2006.11.034

Vancouver

Towers DA, Varea VR. Elementary Lie Algebras and Lie A-Algebras. Journal of Algebra. 2007 Jun 15;312(2):891-901. doi: 10.1016/j.jalgebra.2006.11.034

Author

Towers, David A. ; Varea, Vicente R. / Elementary Lie Algebras and Lie A-Algebras. In: Journal of Algebra. 2007 ; Vol. 312, No. 2. pp. 891-901.

Bibtex

@article{2e84d9b646164d27a7631fad80accae5,
title = "Elementary Lie Algebras and Lie A-Algebras.",
abstract = "A finite-dimensional Lie algebra L over a field F is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. The present paper is primarily concerned with the classification of elementary Lie algebras. In particular, we provide a complete list in the case when F is algebraically closed and of characteristic different from 2,3, reduce the classification over fields of characteristic 0 to the description of elementary semisimple Lie algebras, and identify the latter in the case when F is the real field. Additionally it is shown that over fields of characteristic 0 every elementary Lie algebra is almost algebraic; in fact, if L has no non-zero semisimple ideals, then it is elementary if and only if it is an almost algebraic A-algebra.",
keywords = "Lie algebra, elementary, E-algebra, A-algebra, almost algebraic, ad-semisimple",
author = "Towers, {David A.} and Varea, {Vicente R.}",
note = "The final, definitive version of this article has been published in the Journal, Journal of Algebra 312 (2), 2007, {\textcopyright} ELSEVIER.",
year = "2007",
month = jun,
day = "15",
doi = "10.1016/j.jalgebra.2006.11.034",
language = "English",
volume = "312",
pages = "891--901",
journal = "Journal of Algebra",
publisher = "ELSEVIER ACADEMIC PRESS INC",
number = "2",

}

RIS

TY - JOUR

T1 - Elementary Lie Algebras and Lie A-Algebras.

AU - Towers, David A.

AU - Varea, Vicente R.

N1 - The final, definitive version of this article has been published in the Journal, Journal of Algebra 312 (2), 2007, © ELSEVIER.

PY - 2007/6/15

Y1 - 2007/6/15

N2 - A finite-dimensional Lie algebra L over a field F is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. The present paper is primarily concerned with the classification of elementary Lie algebras. In particular, we provide a complete list in the case when F is algebraically closed and of characteristic different from 2,3, reduce the classification over fields of characteristic 0 to the description of elementary semisimple Lie algebras, and identify the latter in the case when F is the real field. Additionally it is shown that over fields of characteristic 0 every elementary Lie algebra is almost algebraic; in fact, if L has no non-zero semisimple ideals, then it is elementary if and only if it is an almost algebraic A-algebra.

AB - A finite-dimensional Lie algebra L over a field F is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. The present paper is primarily concerned with the classification of elementary Lie algebras. In particular, we provide a complete list in the case when F is algebraically closed and of characteristic different from 2,3, reduce the classification over fields of characteristic 0 to the description of elementary semisimple Lie algebras, and identify the latter in the case when F is the real field. Additionally it is shown that over fields of characteristic 0 every elementary Lie algebra is almost algebraic; in fact, if L has no non-zero semisimple ideals, then it is elementary if and only if it is an almost algebraic A-algebra.

KW - Lie algebra

KW - elementary

KW - E-algebra

KW - A-algebra

KW - almost algebraic

KW - ad-semisimple

U2 - 10.1016/j.jalgebra.2006.11.034

DO - 10.1016/j.jalgebra.2006.11.034

M3 - Journal article

VL - 312

SP - 891

EP - 901

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -