接触李超代数偶部的具有负次数的导子

Derivations with negative degrees for the even part of the Contact Lie superalgebra

F是特征大于3的基域,参数n>3,m>2,并且n是偶数,m是奇数。K,K,W和W1分别表示接触李超代数K(m,n;t)及其偶部和模李超代数W(m,n;t)及其奇部,利用接触李超代数W(m,n;t)偶部的生成元集,通过计算导子在其生成元集上的作用的方法,确定了接触李超代数W(m,n;t)偶部到奇部的Z-次数小于-3的导子,于是接触李超代数K(m,n;t)偶部到奇部的所有具有负Z-次数的导子得以刻画。

The ground field F is assumed of characteristic p 〉 3. The parameters n 〉 3, m 〉 2, and n is even, m is odd. Let K,K, W and Wi denote the Contact Lie superalgebra K（ m, n ;t） and its even part, the modular Lie superalgebra W（ m, n ;t） and its odd part respectively. Using the generating set of the even part of Contact Lie superalgebra K（m, n ;t）, by means of calculating action of derivation on its generating set, derivations with Z-degrees less than-3 of the even part into the odd part for the Contact Lie superalgebra K（ m, n ;t） is determined and then all the derivations with negative Z -degrees of the even part into the odd part for the Contact Lie superalgebra K（ m, n ; t） are determined.