Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I have a question about fixed points of Galois group actions. I am hoping that this is easy for the experts.

Let $k$ be a field of characteristic $0$. Let $K$ be a finite Galois extension of $k$ with Galois group $G$.

Supose that $A$ is any finite dimensional $G$-representation over $k$. Then $G$ acts diagonally on $A\otimes K$. The question is to determine $\dim_{k}(A\otimes K)^{G}$. I am hoping the answer is $\dim_{k}(A)$.

Any ideas on how to attack this problem are more than welcomed.

share|improve this question
add comment

1 Answer 1

up vote 2 down vote accepted

This follows from the fact that $K$ is isomorphic as $G$ module to the free module $k[G]$. (use the existence of a basis of $K$ over $k$ consisting of Galois conjugates.

share|improve this answer
    
That certainly does it. Thanks a lot –  José Manuel Gómez Dec 2 '11 at 22:32
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.