Hilbert Basis Theorem and Finite Generation of Invariants in Symmetric Fusion Categories in Positive Characteristic

2015/07/31 by Siddharth Venkatesh · 1 citation
Mathematics · #math.RT #math.AC

paper · pdf · doi:10.1093/imrn/rnv305

17 pages. v2: Fixed proof of Prop 2.10. Added an example of category not fibering over Verlinde in characteristic 2 and proved main theorems for this category as well

arxiv created 2016/02/16 · arxiv updated 2016/02/17

Abstract

In this paper, we conjecture an extension of the Hilbert basis theorem and the finite generation of invariants to commutative algebras in symmetric finite tensor categories over fields of positive characteristic. We prove the conjecture in the case of semisimple categories and more generally in the case of categories with fiber functors to the characteristic p > 0 Verlinde category of SL₂. We also construct a symmetric finite tensor category \sVec₂ over fields of characteristic 2 and show that it is a candidate for the category of supervector spaces in this characteristic. We further show that \sVec₂ does not fiber over the characteristic 2 Verlinde category of SL₂ and then prove the conjecture for any category fibered over \sVec₂.

Cited by

• Composition algebras in symmetric tensor categories