科研之友
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摘要
A Lie algebra L over a field F is said to be finitary if it is isomorphic to a subalgebra of the Lie algebra of finite rank linear transformations of a vector space over F. A non- zero element a is an element of L is said to be extremal if ad(a)(2)L = Fa By using Baranov ' s classification, it is not difficult to verify that any simple finitary Lie algebra over an algebraically closed field of characteristic 0 is spanned by extremal elements. In this note, we provide a classification- free proof of this result by using Jordan theory instead of representation theory.
- 出版日期2016-12
