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A construction of semisimple tensor categories

Friedrich Knop
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Abstract

Starting from an abelian category A such that every object has only finitely many subobjects we construct a semisimple tensor category T. We show that T interpolates the categories Rep(Aut(p),K) where p runs through certain projective (pro-)objects of A. The main example is A=finite dimensional F_q-vector spaces. Then T can be considered as the category of representations of GL(n,F_q) where n is not a natural number. This work extends a construction of Deligne for symmetric groups.

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Friedrich Knop. 2006-05-13. A construction of semisimple tensor categories. https://doi.org/10.1016/j.crma.2006.05.009

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