141 citations · 314 across the 34 of their papers we have counts for
42 papers
Lie algebras in symmetric tensor categories
Iván Angiono, Agustina Czenky, Pavel Etingof +3
We develop the general theory of Lie algebras in symmetric tensor categories. We prove categorical versions of classical results such as Engel's theorem, Cartan's criterion, and th…
Pivotal Brauer-Picard groupoids and graded extensions
Agustina Czenky, David Jaklitsch, Dmitri Nikshych +4
We develop pivotal and spherical versions of graded extension theory. We define the corresponding analogues of Brauer-Picard -categorical groups and realize them as fixed points…
On the representation type of a finite tensor category
Petter Andreas Bergh, Karin Erdmann, Julia Yael Plavnik +1
Given an exact module category over a finite tensor category with finitely generated cohomology, we show that if there exists an object of complexity at least three, then the categ…
Egyptian fractions for few primes
Agustina Czenky, Emily McGovern, Julia Plavnik +2
We study solutions to the Egyptian fractions equation with the prime factors of the denominators constrained to lie in a fixed set of primes. We evaluate the effectiveness of the g…
Relation between bicrossed products and crossed extensions of fusion categories
Monique Müller, Héctor Martín Peña Pollastri, Julia Plavnik
We show that all crossed extensions defined by Natale can be recovered as duals of bicrossed products of fusion categories. As an application, we prove that any exact factorization…
Relating insplittings of 2-graphs and of textile systems
Samantha Brooker, Priyanga Ganesan, Elizabeth Gillaspy +3
The graphical operation of insplitting is key to understanding conjugacy of shifts of finite type (SFTs) in both one and two dimensions. In this paper, we consider two approaches t…
Generalised Orbifolds and G-equivariantisation
Sebastian Heinrich, Julia Plavnik, Ingo Runkel +1
In a construction motivated by topological field theory, a so-called orbifold datum in a ribbon category allows one to define a new ribbon category $C_{\mathbb{A}}…
On the finite generation of the cohomology of bosonizations
Nicolás Andruskiewitsch, David Jaklitsch, Van C. Nguyen +4
We use deformation sequences of (Hopf) algebras, extending the results of Negron and Pevtsova, to show that bosonizations of some suitable braided Hopf algebras by some suitable fi…
The Classification of Fusion 2-Categories
Thibault D. Décoppet, Peter Huston, Theo Johnson-Freyd +5
We classify (multi)fusion 2-categories in terms of braided fusion categories and group cohomological data. This classification is homotopy coherent -- we provide an equivalence bet…
The Condensed Fiber Product and Zesting
Colleen Delaney, César Galindo, Julia Plavnik +2
We introduce the condensed fiber product of two -crossed braided fusion categories, generalizing existing constructions in the literature. We show that this product is closely r…
On bicrossed product of fusion categories and exact factorizations
Monique Müller, Héctor Martín Peña Pollastri, Julia Plavnik
We introduce the notion of a matched pair of fusion rings and fusion categories, generalizing the one for groups. Using this concept, we define the bicrossed product of fusion ring…
On Frobenius-Schur exponent bounds
Agustina Czenky, Julia Plavnik, Andrew Schopieray
Here we study bounds on the Frobenius-Schur exponent of spherical fusion categories based on their global dimension generalizing bounds from the representation theory of finite-dim…
Integral non-group-theoretical modular categories of dimension
César Galindo, Julia Plavnik, Eric C. Rowell
We construct all integral non-group-theoretical modular categories of dimension , where and are distinct prime numbers, establishing that a necessary and sufficient…
Contragredient Lie algebras in symmetric categories
Iván Angiono, Julia Plavnik, Guillermo Sanmarco
We define contragredient Lie algebras in symmetric categories, generalizing the construction of Lie algebras of the form for a Cartan matrix from the category…
Semisimplification of contragredient Lie algebras
Iván Angiono, Julia Plavnik, Guillermo Sanmarco
We describe the structure and different features of Lie algebras in the Verlinde category, obtained as semisimplification of contragredient Lie algebras in characteristic with…
On modular categories with Frobenius-Perron dimension congruent to 2 modulo 4
Akshaya Chakravarthy, Agustina Czenky, Julia Plavnik
We contribute to the classification of modular categories with . We prove that such categories have group of invert…
Support varieties for finite tensor categories: the tensor product property
Petter Andreas Bergh, Julia Yael Plavnik, Sarah Witherspoon
We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to…
Classification of low-rank odd-dimensional modular categories
Agustina Czenky, William Gvozdjak, Julia Plavnik
We prove that any odd-dimensional modular category of rank at most 23 is pointed. We also show that an odd-dimensional modular category of rank 25 is either pointed, perfect, or eq…
Tambara-Yamagami Categories over the Reals: The Non-Split Case
Julia Plavnik, Sean Sanford, Dalton Sconce
Tambara and Yamagami investigated a simple set of fusion rules with only one non-invertible object, and proved under which circumstances those rules could be given a coherent assoc…
-crossed braided zesting
Colleen Delaney, César Galindo, Julia Plavnik +2
For a finite group , a -crossed braided fusion category is -graded fusion category with additional structures, namely a -action and a -braiding. We develop the notio…
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…
Zesting produces modular isotopes and explains their topological invariants
Colleen Delaney, Sung Kim, Julia Plavnik
We show that the ribbon zesting construction can produce modular isotopes -- different modular fusion categories with the same modular data. The result relies on the observation th…
On odd-dimensional modular tensor categories
Agustina Czenky, Julia Plavnik
We study odd-dimensional modular tensor categories and maximally non-self dual (MNSD) modular tensor categories of low rank. We give lower bounds for the ranks of modular tensor ca…
Braided zesting and its applications
Colleen Delaney, César Galindo, Julia Plavnik +2
We give a rigorous development of the construction of new braided fusion categories from a given category known as zesting. This method has been used in the past to provide categor…