A construction of semisimple tensor categories

Details A construction of semisimple tensor categories A construction of semisimple tensor categories

2006-05-04

arxiv.org/abs/math/0605126v2

C. R. Math. Acad. Sci. Paris 343 (2006) 15-18

Mathematics

Category Theory

v1: 6 pages; v2: 6 pages, slightly shortened, minor changes

Scientific paper

10.1016/j.crma.2006.05.009

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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