Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - The index complex of a maximal subalgebra of a Lie algebra.
AU - Towers, David A.
N1 - 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, © 2011 Cambridge University Press.
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 -