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On the lengths of certain chains of subalgebras in Lie algebras

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On the lengths of certain chains of subalgebras in Lie algebras. / Towers, David.

In: Communications in Algebra, Vol. 42, No. 11, 2014, p. 4778-4789.

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Towers, David. / On the lengths of certain chains of subalgebras in Lie algebras. In: Communications in Algebra. 2014 ; Vol. 42, No. 11. pp. 4778-4789.

Bibtex

@article{d9577962866e4778a7e7d70d0d691942,
title = "On the lengths of certain chains of subalgebras in Lie algebras",
abstract = "In this paper we study the lengths of certain chains of subalgebras of a Lie algebra L: namely, a chief series, a maximal chain of minimal length, a chain of maximal length in which each subalgebra is modular in L, and a chain of maximal length in which each subalgebra is a quasi-ideal of L. In particular we show that, over a field F of characteristic zero, a Lie algebra L with radical R has a maximal chain of subalgebras and a chain of subalgebras all of which are modular in L of the same length if and only if L = R, or ??? and L/R is a direct sum of isomorphic three-dimensional simple Lie algebras.",
keywords = "Chief series, Lie algebras , Maximal chain , Modular subalgebra , Quasi\-ideal",
author = "David Towers",
year = "2014",
doi = "10.1080/00927872.2013.824735",
language = "English",
volume = "42",
pages = "4778--4789",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "11",

}

RIS

TY - JOUR

T1 - On the lengths of certain chains of subalgebras in Lie algebras

AU - Towers, David

PY - 2014

Y1 - 2014

N2 - In this paper we study the lengths of certain chains of subalgebras of a Lie algebra L: namely, a chief series, a maximal chain of minimal length, a chain of maximal length in which each subalgebra is modular in L, and a chain of maximal length in which each subalgebra is a quasi-ideal of L. In particular we show that, over a field F of characteristic zero, a Lie algebra L with radical R has a maximal chain of subalgebras and a chain of subalgebras all of which are modular in L of the same length if and only if L = R, or ??? and L/R is a direct sum of isomorphic three-dimensional simple Lie algebras.

AB - In this paper we study the lengths of certain chains of subalgebras of a Lie algebra L: namely, a chief series, a maximal chain of minimal length, a chain of maximal length in which each subalgebra is modular in L, and a chain of maximal length in which each subalgebra is a quasi-ideal of L. In particular we show that, over a field F of characteristic zero, a Lie algebra L with radical R has a maximal chain of subalgebras and a chain of subalgebras all of which are modular in L of the same length if and only if L = R, or ??? and L/R is a direct sum of isomorphic three-dimensional simple Lie algebras.

KW - Chief series

KW - Lie algebras

KW - Maximal chain

KW - Modular subalgebra

KW - Quasi\-ideal

U2 - 10.1080/00927872.2013.824735

DO - 10.1080/00927872.2013.824735

M3 - Journal article

VL - 42

SP - 4778

EP - 4789

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 11

ER -