首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Automorphisms and Derivations of Certain Solvable Lie Algebras Over Commutative Rings
Authors:Zhengxin Chen
Institution:1. School of Mathematics and Computer Science , Fujian Normal University , Fuzhou , P.R. China czxing@163.com
Abstract:Let L be a finite-dimensional complex simple Lie algebra, L ? be the ?-span of a Chevalley basis of L, and L R  = R ?? L ? be a Chevalley algebra of type L over a commutative ring R with identity. Let ?(R) be the solvable subalgebra of L R spanned by the basis elements of the maximal toral subalgebra and the root vectors associated with positive roots. In this article, we prove that under some conditions for R, any automorphism of ?(R) is uniquely decomposed as a product of a graph automorphism, a diagonal automorphism and an inner automorphism, and any derivation of ?(R) is uniquely decomposed as a sum of an inner derivation induced by root vectors and a diagonal derivation. Correspondingly, the automorphism group and the derivation algebra of ?(R) are determined.
Keywords:Automorphism  Chevalley algebra  Commutative ring  Derivation  Solvable Lie algebra
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号