6 papers
Modular tensor categories, subcategories, and Galois orbits
Julia Plavnik, Andrew Schopieray, Zhiqiang Yu +1
We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes a characterization of fusion su…
Classification of super-modular categories
Paul Bruillard, Julia Yael Plavnik, Eric C. Rowell +1
We develop categorical and number theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular cat…
Support varieties for finite tensor categories: Complexity, realization, and connectedness
Petter Andreas Bergh, Julia Yael Plavnik, Sarah Witherspoon
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 projecti…
Completion for braided enriched monoidal categories
Scott Morrison, David Penneys, Julia Plavnik
Monoidal categories enriched in a braided monoidal category are classified by braided oplax monoidal functors from to the Drinfeld centers of ordinary m…
Cohomology of finite tensor categories: duality and Drinfeld centers
Cris Negron, Julia Yael Plavnik
We consider the finite generation property for cohomology of a finite tensor category C, which requires that the self-extension algebra of the unit Ext*_C(1,1) is a finitely genera…
Fusion Rules for Permutation Gauging
Cain Edie-Michell, Corey Jones, Julia Plavnik
In this note, we examine the gauging of the permutation action on the tensor square of a modular tensor category. When has no nontrivial inve…