(3,1)-维李2-代数的分类

Classification of(3,1)-dimensional Lie 2-algebras

当V0的维数是3,V1的维数是1时,我们称李2-代数(V_(1)→dV_(0),l_(2),l_(3))为一个(3,1)-维李2-代数.我们分别给出了(3,1)-维李2-代数在等价、同构、线性同构三种关系下的分类.有趣的是,在这种情况下,等价和同构下的分类是一致的.

A Lie 2-algebra(V_(1)→dV_(0),l_(2),l_(3))with dimRV0=3 and dimRV=1 is called a(3,1)-dimensional Lie 2-algebra.We give classifications of(3,1)-dimensional Lie 2-algebras up to equivalences,isomorphisms,and linear isomorphisms,respectively.It is surprising that classifications up to equivalences and isomorphisms are the same for this case.