Heisenberg超代数的导子代数

J4 ›› 2011, Vol. 49 ›› Issue (03): 419-423.

Heisenberg超代数的导子代数

周佳¹, 陈良云²

1. 吉林农业大学信息技术学院, 长春 130118|2. 东北师范大学数学与统计学院, 长春 130024

收稿日期:2010-07-07 出版日期:2011-05-26 发布日期:2011-06-15
通讯作者: 陈良云 E-mail:chenly640@nenu.edu.cn

Derivation Algebra of Heisenberg Superalgebra

ZHOU Jia¹, CHEN Liangyun²

1. School of Information and Technology, Jilin Agricultural University, Changchun 130118, China;2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received:2010-07-07 Online:2011-05-26 Published:2011-06-15
Contact: CHEN Liangyun E-mail:chenly640@nenu.edu.cn

摘要/Abstract

摘要：

以Heisenberg超代数H的导子在基底上的表示矩阵为工具, 得到了关于复数域 C上的有限维Heisenberg超代数H的导子代数和全形的结论: H的导子代数Der H是单完备的李超代数, 而H的全形h(H)不是完备李超代数.

关键词: Heisenberg超代数, 导子代数, 完备李超代数, 全形

Abstract:

With matrix of the derivation of Heisenberg superalgebra H relative to the basis of H as a tool, we obtained some
properties of the derivation algebra and holomorph of the finite dimensional Heisenberg superalgebra over the complex field C. The derivation algebra ofH is simple complete, while the holomorph of H is not complete Liesuperalgebras.

Key words: Heisenberg superalgebras, derivation algebra, complete Liesuperalgebras, holomorph

中图分类号:

O152.5

周佳, 陈良云. Heisenberg超代数的导子代数[J]. J4, 2011, 49(03): 419-423.

ZHOU Jia, CHEN Liang-Yun. Derivation Algebra of Heisenberg Superalgebra[J]. J4, 2011, 49(03): 419-423.