On the derived algebra of a centraliser

✍ Scribed by Oksana Yakimova

• Publisher: Elsevier Science
• Year: 2010
• Tongue: French
• Weight: 145 KB
• Volume: 134
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/j.bulsci.2010.03.005

✦ Synopsis

Let g be a classical Lie algebra, e ∈ g a nilpotent element and g e ⊂ g the centraliser of e. We prove that g e = [g e , g e ] if and only if e is rigid. It is also shown that if e ∈ [g e , g e ], then the nilpotent radical of g e coincides with [g(1) e , g e ], where g(1) e ⊂ g e is an eigenspace of a characteristic of e corresponding to the eigenvalue 1.