Simplicity of twists of abelian varieties
We give some easy necessary and sufficient criteria for twists of abelian varieties by Artin representations to be simple.
Brauer relations in finite groups
If is a non-cyclic finite group, non-isomorphic -sets may give rise to isomorphic permutation representations . Equivalently, the map from the Burnside ring to the rational representation ring of has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave–Bouc classification in the case of -groups.
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