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

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

2007-11-06

arxiv.org/abs/0711.0795v4

Algebras and Representation Theory 13 (2010), no. 3, 271-301

Mathematics

Representation Theory

final version, to appear in "Algebras and Representation Theory"

Scientific paper

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.

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