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C-Ideals of Lie Algebras.

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

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C-Ideals of Lie Algebras. / Towers, David A.
In: Communications in Algebra, Vol. 37, No. 12, 12.2009, p. 4366-4373.

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

Harvard

Towers, DA 2009, 'C-Ideals of Lie Algebras.', Communications in Algebra, vol. 37, no. 12, pp. 4366-4373. https://doi.org/10.1080/00927870902829023

APA

Towers, D. A. (2009). C-Ideals of Lie Algebras. Communications in Algebra, 37(12), 4366-4373. https://doi.org/10.1080/00927870902829023

Vancouver

Towers DA. C-Ideals of Lie Algebras. Communications in Algebra. 2009 Dec;37(12):4366-4373. doi: 10.1080/00927870902829023

Author

Towers, David A. / C-Ideals of Lie Algebras. In: Communications in Algebra. 2009 ; Vol. 37, No. 12. pp. 4366-4373.

Bibtex

@article{a26d8ba6704642b3aa49cc78b9904916,
title = "C-Ideals of Lie Algebras.",
abstract = "A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B \cap C \leq B_L, where B_L is the largest ideal of L contained in B. This is analogous to the concept of c-normal subgroup, which has been studied by a number of authors. We obtain some properties of c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every one-dimensional subalgebra is a c-ideal.",
keywords = "Lie algebras, c-ideal, nilpotent, solvable, supersolvable, Frattini ideal.",
author = "Towers, {David A.}",
note = "The final, definitive version of this article has been published in the Journal, Communications in Algebra, 37 (12), 2009, {\textcopyright} Informa Plc",
year = "2009",
month = dec,
doi = "10.1080/00927870902829023",
language = "English",
volume = "37",
pages = "4366--4373",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "12",

}

RIS

TY - JOUR

T1 - C-Ideals of Lie Algebras.

AU - Towers, David A.

N1 - The final, definitive version of this article has been published in the Journal, Communications in Algebra, 37 (12), 2009, © Informa Plc

PY - 2009/12

Y1 - 2009/12

N2 - A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B \cap C \leq B_L, where B_L is the largest ideal of L contained in B. This is analogous to the concept of c-normal subgroup, which has been studied by a number of authors. We obtain some properties of c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every one-dimensional subalgebra is a c-ideal.

AB - A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B \cap C \leq B_L, where B_L is the largest ideal of L contained in B. This is analogous to the concept of c-normal subgroup, which has been studied by a number of authors. We obtain some properties of c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every one-dimensional subalgebra is a c-ideal.

KW - Lie algebras

KW - c-ideal

KW - nilpotent

KW - solvable

KW - supersolvable

KW - Frattini ideal.

U2 - 10.1080/00927870902829023

DO - 10.1080/00927870902829023

M3 - Journal article

VL - 37

SP - 4366

EP - 4373

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 12

ER -