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Michi’s blog » Question for the mathematical audience

 Question for the mathematical audience

  • April 20th, 2006
  • 3:44 pm

I have now been staring at this particular sentence for way too long, and thus will start using any and all communication lines I can find to get assistance. Either I’m being way too stupid, or the author neglects to mention some salient detail.

Setup: \phi\colon G^\prime\to G is a group homomorphism, A\in kG-\operator{mod}, A^\prime\in kG^\prime-\operator{mod}. A can be given the structure of a kG^\prime-module by pulling back through \phi, i.e. we define g^\prime a:=\phi(g^\prime)a for g^\prime\in G^\prime and a\in A.

So far it’s all crystal clear for me. However, it then turns out that we’re highly interested in using a morphism f\in\operator{Hom}_G(A,A^\prime) and I cannot for the life of me find out how such beasts are guaranteed to exist. If it where f\in\operator{Hom}_{G^\prime}(A,A^\prime), I wouldn’t have any problems with it; but then the stuff I need/want to do with it don’t work out.

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