Galois Algebras and Monoidal Functors between Categories of Representations of Finite Groups

We use relations between Galois algebras and monoidal functors to describe monoidal functors between categories of representations of finite groups. We pay special attention to two kinds of these monoidal functors: monoidal functors to vector spaces and monoidal equivalences between categories of representations. The functors of the second kind induce isomorphisms of character tables. We show that pairs of groups with the same character table obtained in this way are a generalization of the construction proposed by B. Fischer (1988, Rend. Circ. Mat. Palermo (2) Suppl.19, 71–77).