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 - 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 -