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

Research output: Contribution to journal › Journal article

Towers, D 2014, 'On the lengths of certain chains of subalgebras in Lie algebras', *Communications in Algebra*, vol. 42, no. 11, pp. 4778-4789. https://doi.org/10.1080/00927872.2013.824735

Towers, D. (2014). On the lengths of certain chains of subalgebras in Lie algebras. *Communications in Algebra*, *42*(11), 4778-4789. https://doi.org/10.1080/00927872.2013.824735

Towers D. On the lengths of certain chains of subalgebras in Lie algebras. Communications in Algebra. 2014;42(11):4778-4789. https://doi.org/10.1080/00927872.2013.824735

@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",

}

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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 -