A question from group homology:
Let A and B be G - modules. Why is their tensor product over the integers (which I denote A@B) naturally a G - module? I have read that the natural action of G on A@B is g(a@b)=ga@gb however, I am uncertain as to why (g+h)(a@b)=g(a@b)+h(a@b).
A question from representation theory:
Let k be a field of characteristic 0. Let A and B be k[G] - modules. Then is A tensor B (over k) naturally a k[G] - module with the action defined as in the first question.
Thanks for any replies and sorry for the lack of latex.