Generators of simple Lie algebras II
Jean-Marie Bois

TL;DR
This paper investigates the generation properties of simple Lie algebras, showing that certain Cartan type algebras do not possess the 'one-and-a-half generation' property, contrasting with classical Lie algebras.
Contribution
It extends previous work by analyzing the generation properties of Cartan type simple Lie algebras in arbitrary characteristic.
Findings
Cartan type S, H, K Lie algebras lack the 'one-and-a-half' generation property
Classical Lie algebras can have this property, unlike Cartan types
Study of centralisers in Cartan type Lie algebras underpins the results
Abstract
This paper is a continuation of earlier work on generators of simple Lie algebras in arbitrary characteristic (see arXiv:0708.1711). We show that, in contrast to classical Lie algebras, simple graded Lie algebras of Cartan type S,H or K never enjoy the 'one-and-a-half generation' property. The methods rely on a study of centralisers in Cartan type Lie algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry
