Torus型李代数的泛中心扩张

Universal Central Extension for Torus Type Lie Algebra

令Γ=Z2\{0},F是任意特征为0的域.李代数L是F上由xm,E(m)线性生成,其中李关系由文中式(1)给出.Xue的文章是通过求李代数的二上同调群来推出该李代数的泛中心扩张,本文是先给出李代数L一个中心扩张,然后证明所给出的中心扩张同构于L的泛中心扩张.

Let Γ=Z^2／{0},and F be any field with characteristic O. A give by （1） is defined. In Xiffs paper,the universal central extension of L L. In this paper,a central extension of L is given and that it is isomorpic Lie algebra L： =spanp {x^m ,E（m） [m∈F} with Lie bracket was obtained by computing the second cohomology group of to the universal central extension of L is proved.