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In: Proceedings of the Edinburgh Mathematical Society, Vol. 54, No. 2, 01.06.2011, p. 531-542.

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

Towers, DA 2011, 'The index complex of a maximal subalgebra of a Lie algebra.', *Proceedings of the Edinburgh Mathematical Society*, vol. 54, no. 2, pp. 531-542. https://doi.org/10.1017/S0013091509001035

Towers, D. A. (2011). The index complex of a maximal subalgebra of a Lie algebra. *Proceedings of the Edinburgh Mathematical Society*, *54*(2), 531-542. https://doi.org/10.1017/S0013091509001035

Towers DA. The index complex of a maximal subalgebra of a Lie algebra. Proceedings of the Edinburgh Mathematical Society. 2011 Jun 1;54(2):531-542. doi: 10.1017/S0013091509001035

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title = "The index complex of a maximal subalgebra of a Lie algebra.",

abstract = "Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of M is called the index complex of M in L. We use this concept to investigate the influence of the maximal subalgebras on the structure of a Lie algebra, in particular finding new characterisations of solvable and supersolvable Lie algebras.",

keywords = "Lie algebras, maximal subalgebra, index complex, ideal index, solvable, supersolvable, Frattini ideal.",

author = "Towers, {David A.}",

note = "http://journals.cambridge.org/action/displayJournal?jid=PEM The final, definitive version of this article has been published in the Journal, Proceedings of The Edinburgh Mathematical Society, 54 (2), pp 531-542 2011, {\textcopyright} 2011 Cambridge University Press.",

year = "2011",

month = jun,

day = "1",

doi = "10.1017/S0013091509001035",

language = "English",

volume = "54",

pages = "531--542",

journal = "Proceedings of the Edinburgh Mathematical Society",

issn = "0013-0915",

publisher = "Cambridge University Press",

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AU - Towers, David A.

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PY - 2011/6/1

Y1 - 2011/6/1

N2 - Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of M is called the index complex of M in L. We use this concept to investigate the influence of the maximal subalgebras on the structure of a Lie algebra, in particular finding new characterisations of solvable and supersolvable Lie algebras.

AB - Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of M is called the index complex of M in L. We use this concept to investigate the influence of the maximal subalgebras on the structure of a Lie algebra, in particular finding new characterisations of solvable and supersolvable Lie algebras.

KW - Lie algebras

KW - maximal subalgebra

KW - index complex

KW - ideal index

KW - solvable

KW - supersolvable

KW - Frattini ideal.

U2 - 10.1017/S0013091509001035

DO - 10.1017/S0013091509001035

M3 - Journal article

VL - 54

SP - 531

EP - 542

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 2

ER -