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We study finite-dimensional representations of hyper loop algebras overnon-algebraically closed fields. The main results concern the classification ofthe irreducible representations, the construction of the Weyl modules, basechange, tensor products of irreducible and Weyl modules, and the blockdecomposition of the underlying abelian category. Several results areinterestingly related to the study of irreducible representations of polynomialalgebras and Galois theory.

Finite-Dimensional Representations of Hyper Loop Algebras Over Non-Algebraically Closed Fields