华东师范大学学报(自然科学版) ›› 2003, Vol. 2003 ›› Issue (1): 21-24.

• 论文 • 上一篇    下一篇

gl∞(C)的导子代数

夏利猛；杨恒云；林磊   

  1. 华东师范大学 数学系，上海 200062
  • 收稿日期:2001-04-11 修回日期:2002-06-26 出版日期:2003-03-25 发布日期:2003-03-25

The Derivation Algebra of gl∞(C)

XIA Li-meng; YANG Heng-yun; LIN Lei

  

  1. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2001-04-11 Revised:2002-06-26 Online:2003-03-25 Published:2003-03-25

摘要： 该文证明了只有有限个非零元的无限矩阵构成的李代数的导子代数同构于每行每列都有限个非零元的无限矩阵构成的李代数模去其中心所成的商。同时证明这个商代数是完备李代数。

关键词: 导子, 导子代数, 李代数, 导子, 导子代数, 李代数

Abstract: In this paper, it is proved that the derivation algebra of the Lie algebra of infinite matrices with finite nonzero entries is isomorphic to the quotient of the Lie algebra of infinite matrices with finite nonzero entries in each row and in each column nodulo its center. It os also proved that this quotient is a complete Lie algebra.

Key words: derivation algebra, Lie algebra, derivation, derivation algebra, Lie algebra