Home > Research > Publications & Outputs > Two Generator Subalgebras Of Lie Algebras.

Research

Associated organisational unit

Electronic data

Links

Text available via DOI:

Keywords

View graph of relations

Two Generator Subalgebras Of Lie Algebras.

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

Published

Standard

Two Generator Subalgebras Of Lie Algebras. / Bowman, Kevin; Towers, David A.; Varea, Vicente R.
In: Linear and Multilinear Algebra, Vol. 55, No. 5, 09.2007, p. 429-438.

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

Harvard

Bowman, K, Towers, DA & Varea, VR 2007, 'Two Generator Subalgebras Of Lie Algebras.', Linear and Multilinear Algebra, vol. 55, no. 5, pp. 429-438. https://doi.org/10.1080/03081080500472996

APA

Bowman, K., Towers, D. A., & Varea, V. R. (2007). Two Generator Subalgebras Of Lie Algebras. Linear and Multilinear Algebra, 55(5), 429-438. https://doi.org/10.1080/03081080500472996

Vancouver

Bowman K, Towers DA, Varea VR. Two Generator Subalgebras Of Lie Algebras. Linear and Multilinear Algebra. 2007 Sept;55(5):429-438. doi: 10.1080/03081080500472996

Author

Bowman, Kevin ; Towers, David A. ; Varea, Vicente R. / Two Generator Subalgebras Of Lie Algebras. In: Linear and Multilinear Algebra. 2007 ; Vol. 55, No. 5. pp. 429-438.

Bibtex

@article{9a79c05befc84eea9246b5d6ccb0e72c,
title = "Two Generator Subalgebras Of Lie Algebras.",
abstract = "In [14] Thompson showed that a finite group G is solvable if and only if every twogenerated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al. [10] have shown that the analogue holds for finite-dimensional Lie algebras over infinite fields of characteristic greater than 5. It is a natural question to ask to what extent the two-generated subalgebras determine the structure of the algebra. It is to this question that this paper is addressed. Here, we consider the classes of strongly-solvable and of supersolvable Lie algebras, and the property of triangulability.",
keywords = "Lie algebra, two generator, solvable, supersolvable, triangulable",
author = "Kevin Bowman and Towers, {David A.} and Varea, {Vicente R.}",
note = "The final, definitive version of this article has been published in the Journal, Linear and Multilinear Algebra, 55 (5), 2007, {\textcopyright} Informa Plc",
year = "2007",
month = sep,
doi = "10.1080/03081080500472996",
language = "English",
volume = "55",
pages = "429--438",
journal = "Linear and Multilinear Algebra",
issn = "1563-5139",
publisher = "Taylor and Francis Ltd.",
number = "5",

}

RIS

TY - JOUR

T1 - Two Generator Subalgebras Of Lie Algebras.

AU - Bowman, Kevin

AU - Towers, David A.

AU - Varea, Vicente R.

N1 - The final, definitive version of this article has been published in the Journal, Linear and Multilinear Algebra, 55 (5), 2007, © Informa Plc

PY - 2007/9

Y1 - 2007/9

N2 - In [14] Thompson showed that a finite group G is solvable if and only if every twogenerated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al. [10] have shown that the analogue holds for finite-dimensional Lie algebras over infinite fields of characteristic greater than 5. It is a natural question to ask to what extent the two-generated subalgebras determine the structure of the algebra. It is to this question that this paper is addressed. Here, we consider the classes of strongly-solvable and of supersolvable Lie algebras, and the property of triangulability.

AB - In [14] Thompson showed that a finite group G is solvable if and only if every twogenerated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al. [10] have shown that the analogue holds for finite-dimensional Lie algebras over infinite fields of characteristic greater than 5. It is a natural question to ask to what extent the two-generated subalgebras determine the structure of the algebra. It is to this question that this paper is addressed. Here, we consider the classes of strongly-solvable and of supersolvable Lie algebras, and the property of triangulability.

KW - Lie algebra

KW - two generator

KW - solvable

KW - supersolvable

KW - triangulable

U2 - 10.1080/03081080500472996

DO - 10.1080/03081080500472996

M3 - Journal article

VL - 55

SP - 429

EP - 438

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 1563-5139

IS - 5

ER -