This question comes from my notes, thus slightly unusual structure.

Let's use the notation of [A=>B] for Hom(A, B). Take a 1-dimensional algebraic torus Gm and higher-dimensional torus T.

Out of four expressions like [Gm => [Gm=>T]] etc. half give back T (*), others the dual torus TV, in the sense that X*(T) := [Gm => T] = [TV => Gm] =: X*(TV).

To prove equality (*) use

   (**)       A \otimes [B=>B] ==== [[A=>B] => B]

for B = Gm.

Question: Is there an example of algebraic group B, other than Gm, for which the identity (**) is also true (or perhaps true in some other sense)?

(Note that would be true if we could write [X => Y] = X* \otimes Y whenever X and Y are groups, in analogy with vector spaces, but I don't think you can do this to groups)