Cartan型模李超代数S(m,n;t)的中心扩张（英文）

THE CENTRAL EXTENSION OF THE MODULAR LIE SUPERALGEBRA OF CARTAN TYPE S(m,n;t)

本文研究了特征为素数p>2的有限维Special李超代数S(m,n;t)的中心扩张.通过计算从S(m,n;t)到S(m,n;t)~*的斜外导子,得到二阶上同调群H^2(S(m,n;t),F)是平凡的.应用此结果,可得S(m,n;t)的中心扩张是平凡的.

In this paper,we study the central extension of the finite-dimensional special Lie superalgebra S（m,n;t）,where F is an algebracially closed field of prime characteristic p〉2.By computing the skew outer derivations of S（m,n;t） to S（m,n;t）^＊,we obtain the second cohomology group H^2（S（m,n;t）,F） is trivial.As applications,we determine the central extension of S（m,n;t）is trivial.