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A construction of semisimple tensor categories

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arxiv math/0605126 v2 pith:V7DUOC5O submitted 2006-05-04 math.CT math.RT

Friedrich Knop This is my paper · ORCID
classification math.CTmath.RT
keywords categorycategoriesconstructionsemisimpletensorabeliancertainconsidered
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 23 citations worldwide. Full citation record

  1. Classical interpolation categories

    math.RT 2025-07 conditional novelty 7.0 of 10

    Ultraproduct and oligomorphic-group constructions of interpolation categories for finite classical groups agree, and the categories depend only on a parameter t, with an additional parity label in the orthogonal case.

  2. Growth problems in diagram categories

    math.RT 2025-03 unverdicted novelty 4.0 of 10

    Derives asymptotic formulas for the growth rate of the number of summands in tensor powers of the generating object in semisimple diagram/interpolation categories.

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