Support varieties for finite tensor categories: Complexity, realization, and connectedness
Quantum Algebra
2020-06-04 v3 Representation Theory
Abstract
We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension. Then we show that every conical subvariety of the support variety of the unit object may be realized as the support variety of an object. Finally, we show that the support variety of an indecomposable object is connected.
Cite
@article{arxiv.1905.07031,
title = {Support varieties for finite tensor categories: Complexity, realization, and connectedness},
author = {Petter Andreas Bergh and Julia Yael Plavnik and Sarah Witherspoon},
journal= {arXiv preprint arXiv:1905.07031},
year = {2020}
}
Comments
22 pages, added algebraically closed hypothesis