关于自同构作用下的不变元

On Invariant Elements under Automorphic Actions

中文关键词:  自同构  不变元  Hopf代数  以group－like元素．

英文关键词:automorphism  invariant elements  Hopf algebras  group-like elements.

中文摘要:

      文章主要讨论了代数（环）、（双）Ｈｏｐｆ代数中自同构作用下不变元素的性质，得到一些新的结果：设Ａ是有限维半单代数，则ＡｕｔＡ作用下的不变元属于中心，并且举出反例说明这个性质不能一般化到有限维代数、有限维半单（双）Ｈｏｐｆ代数．

英文摘要:

      The aim of the paper is to study the property of invariant elements(or fixed ele-ments) under antomorphic actions in algebras and Hopf algebras. It is shown that if Ais a finite d imensional semisimple algebra over a field K,then the element fixed by allautomorphsims of A is in the center of A. An example is given to show that this conclu-sion cannot be generalized to Hopf algebras. Some counter-examples of other systems areconstructed.