素特征域上无扭仿型李代数的实现

ON A FIELD F OF OHF≠0, 2, 3. THE REALIZATION OF NON-TWISETED AFFINE LIE ALGEBRAS

在有单位元的可换环上研究仿型李代数有两种定义，一种是应用生成元和定义关系的方法［１］；另一种是应用Ｃｈｅｖａｌｌｅｙ生成元的张量扩张的方法［２］．本文做了以下两方面的工作：（ｉ）＃第一种方法应用到罗朗多项式环上，由素特征ｐ≠２，３的域上典型单李代数出发进行一维中心扩张得到无扭仿型李代数的实现，定理２．６．（ｉｉ）证明了以上两种方法定义的李代数在素特征ｐ≠２，３的域上是同构的．

About defining and research Lie algebra correSPonding to generalized Cartan matrix on the field with finite characterisation gave two definition of different forms in [1] and [2]respectively. This paper gives mainly the following results: (i) proves the equivalue of the two definition forms in [1] and [2] for the non-twisted Affine Lie algebra. (ii) shows the realization or non-twisted Affine Lie algebras.