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Cartan型模李超代数S(m,n;t)的中心扩张
引用本文:谢文娟,魏竹.Cartan型模李超代数S(m,n;t)的中心扩张[J].数学杂志,2016,36(1):77-86.
作者姓名:谢文娟  魏竹
作者单位:哈尔滨师范大学数学科学学院, 黑龙江 哈尔滨 150025,东北师范大学数学与统计学院, 吉林 长春 130024
基金项目:Supported by Scientific Research Fund of Heilongjiang Provincial Education Department (12521157).
摘    要: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H2(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.

关 键 词:Cartan型模李超代数  导子  斜导子  上同调群
收稿时间:2013/6/30 0:00:00
修稿时间:2014/2/24 0:00:00

THE CENTRAL EXTENSION OF THE MODULAR LIE SUPERALGEBRA OF CARTAN TYPE S(m, n;t)
XIE Wen-juan and WEI Zhu.THE CENTRAL EXTENSION OF THE MODULAR LIE SUPERALGEBRA OF CARTAN TYPE S(m, n;t)[J].Journal of Mathematics,2016,36(1):77-86.
Authors:XIE Wen-juan and WEI Zhu
Institution:School of Math. Sciences, Harbin Normal University, Harbin 150025, China and School of Math. and Statistics, Northeast Normal University, Changchun 130024, China
Abstract: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 H2(S(m,n;t), F) is trivial. As applications, we determine the central extension of S(m,n;t) is trivial.
Keywords:modular Lie superalgebra of Cartan type  derivation  skew derivation  cohomology group
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