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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 - Lie algebras with nilpotent length greater than that of each of their subalgebras
AU - Towers, David Anthony
PY - 2017/6
Y1 - 2017/6
N2 - The main purpose of this paper is to study the finite-dimensional solvable Lie algebras described in its title, which we call minimal non-N . To facilitate this we investigate solvable Lie algebras of nilpotent length k, and of nilpotent length ≤ k, and extreme Lie algebras, which have the property that their nilpotent length is equal to the number of conjugacy classes of maximal subalgebras. We characterise the minimal non-N Lie algebras in which every nilpotent subalgebra is abelian, and those of solvability index ≤ 3.
AB - The main purpose of this paper is to study the finite-dimensional solvable Lie algebras described in its title, which we call minimal non-N . To facilitate this we investigate solvable Lie algebras of nilpotent length k, and of nilpotent length ≤ k, and extreme Lie algebras, which have the property that their nilpotent length is equal to the number of conjugacy classes of maximal subalgebras. We characterise the minimal non-N Lie algebras in which every nilpotent subalgebra is abelian, and those of solvability index ≤ 3.
KW - Lie algebras
KW - Solvable
KW - Nilpotent series
KW - Nilpotent length
KW - Chief factor
KW - Extreme
KW - Nilregular
KW - Characteristic ideal
KW - A-algebra
U2 - 10.1007/s10468-016-9662-z
DO - 10.1007/s10468-016-9662-z
M3 - Journal article
VL - 20
SP - 735
EP - 750
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
SN - 1386-923X
IS - 3
ER -