The Wielandt Subalgebra of a Lie Algebra

Date

2003

Authors

Barnes, Donald W
Groves, Daniel

Journal Title

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Publisher

Australian Mathematics Publishing Association

Abstract

Following the analogy with group theory, we define the Wielandt subalgebra of a finite-dimensional Lie algebra to be the intersection of the normalisers of the subnormal subalgebras. In a non-zero algebra,this is a non-zero ideal if the ground field has characteristic 0 or if the derived algebra is nilpotent, allowing the definition of the Wielandt series. For a Lie algebra with nilpotent derived algebra, we obtain a bound for the derived length in terms of the Wielandt length and show this bound to be best possible. We also characterise the Lie algebras with nilpotent derived algebra and Wielandt length 2.

Description

Keywords

Keywords: Lie algebras; Subnormal subalgebras

Citation

Source

Journal of the Australian Mathematical Society

Type

Journal article

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