Pontrjagin空间上J.V.N代数的导子  

DERIVATIONS OF J.V.N-ALGEBRAS ON THE PONTRJAGIN SPACES

作　　者：杨海涛[1] 

机构地区：[1]同济大学应用数学系,上海200092

出　　处：《数学年刊（A辑）》2005年第1期105-112,共8页Chinese Annals of Mathematics

摘　　要：本文证明Pontrjagin空间上非退化的J.V.N代数的导子是内的等价于它在该代数的奇异部分上 的限制为零.对退化的J.V.N代数,证明了Ⅱ1空间第0,Ⅱa和Ⅲa类J.V.N代数上的导子是内 的.通过构造例子说明了第Ⅰ,Ⅱb和Ⅲb类对称代数上的导子一般不是内的.This paper shows that a necessary and sufficient condition for derivation δ of non-degerate J.V.N-algebras A on the Pontrjagin spases to be inner is that restriction of δ on singular part of algebra A be null. For the degerate J.V.N algebras,the authors shows that derivation of J.V.N algebras in 0,Ⅱ0 and Ⅲ0 class on the Ⅰ1 spaces are inner, and use of examples to show that derivations of algebras in Ⅰ, Ⅱb and Ⅲb, class are not inner.

关 键 词：PONTRJAGIN空间 J.V.N代数 导子 内导子 

分 类 号：O177.5[理学—数学]