Tensor envelopes of regular categories
| dc.creator | Knop, Friedrich | |
| dc.date | 2006-10-18 | |
| dc.date | 2007-04-03 | |
| dc.date.accessioned | 2026-07-07T08:30:38Z | |
| dc.date.available | 2026-07-07T08:30:38Z | |
| dc.description | We extend the calculus of relations to embed a regular category A into a family of pseudo-abelian tensor categories T(A,d) depending on a degree function d. Under the condition that all objects of A have only finitely many subobjects, our main results are as follows: 1. Let N be the maximal proper tensor ideal of T(A,d). We show that T(A,d)/N is semisimple provided that A is exact and Mal'cev. Thereby, we produce many new semisimple, hence abelian, tensor categories. 2. Using lattice theory, we give a simple numerical criterion for the vanishing of N. 3. We determine all degree functions for which T(A,d) is Tannakian. As a result, we are able to interpolate the representation categories of many series of profinite groups such as the symmetric groups S_n, the hyperoctahedral groups S_n\semidir Z_2^n, or the general linear groups GL(n,F_q) over a fixed finite field. This paper generalizes work of Deligne, who first constructed the interpolating category for the symmetric groups S_n. It also extends (and provides proofs for) a previous paper math.CT/0605126 on the special case of abelian categories. | |
| dc.description | v1: 52 pages; v2: 52 pages, proof of Lemma 7.2 fixed, otherwise minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0610552 | |
| dc.identifier | http://arxiv.org/abs/math/0610552 | |
| dc.identifier | Adv. Math. 214 (2007) 571-617 | |
| dc.identifier | doi:10.1016/j.aim.2007.03.001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138287 | |
| dc.subject | Category Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 18B10; 18D10; 18E10; 20G05 | |
| dc.title | Tensor envelopes of regular categories | |
| dc.type | text |