On Invariant Elements under Automorphic Actions

Abstract:

      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.