  We study finite-dimensional representations of hyper loop algebras over
non-algebraically closed fields. The main results concern the classification of
the irreducible representations, the construction of the Weyl modules, base
change, tensor products of irreducible and Weyl modules, and the block
decomposition of the underlying abelian category. Several results are
interestingly related to the study of irreducible representations of polynomial
algebras and Galois theory.
