可完备化的广义Heisenberg代数

Completable of Generalized Heisenberg Algebras

主要研究了广义Heisenberg代数的性质和分类,给出了它的代数结构,即它是一类特殊的二步幂零李代数,并给出广义Heisenberg代数在实数域上可完备化的充要条件是它的复化李代数可完备化。在此基础上,证明了当广义Heisenberg代数的中心维数dimc(n)=1,2,3时,它是可完备化的幂零李代数。

Mainly studies the properties and classification of generalized Heisenberg algebras, the algebraic structure of it is given which is a special class of two step nilpotent Lie algebras. And generalized Heisenberg algebras in the real domain necessary and suf ficient condition for complete is its complex Lie algebra can be complete. And proves that the generalized Heisenberg algebras with the dimension of center no more than 3 are eompletable Lie algebras.