一类三维Lie代数分类的进一步探讨

A Further Analysis of Three-dimensional Lie Algebra and Its Classification

讨论了满足dim[L,L]=2的3维Lie代数L分类的细节.结果表明:并不是在任何基底下L都能写成标准形式,同时给出了能够写成标准形式的基底之间的变换的充要条件.并由此给出,在标准形式下两两互不同构的Lie代数的正确分类.

The article makes a detailed study of the L classification of three-dimensional Lie algebra which satisfies the equation that dim[L,L]=2, Results show that L can be written in the canonical form, but not under any basis. The necessary and sufficient conditions for L to be written in such a form between the bases are given, and thus the correct classification for two non-isomorphic Lie algebras in this form is also given.