# Computing associators of endomorphism fusion categories

@inproceedings{Barter2021ComputingAO, title={Computing associators of endomorphism fusion categories}, author={Daniel Barter and Jacob C. Bridgeman and Ramona Wolf}, year={2021} }

Many applications of fusion categories, particularly in physics, require the associators or F symbols to be known explicitly. Finding these matrices typically involves solving vast systems of coupled polynomial equations in large numbers of variables. In this work, we present an algorithm that allows associator data for some category with unknown associator to be computed from a Morita equivalent category with known data. Given a module category over the latter, we utilize the representation…

## References

SHOWING 1-10 OF 22 REFERENCES

On fusion categories

- Mathematics
- 2002

Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show…

Finite tensor categories

- Mathematics
- 2003

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our…

Quantum Subgroups of the Haagerup Fusion Categories

- Mathematics
- 2012

We answer three related questions concerning the Haagerup subfactor and its even parts, the Haagerup fusion categories. Namely we find all simple module categories over each of the Haagerup fusion…

Module categories, weak Hopf algebras and modular invariants

- Mathematics
- 2001

AbstractWe develop a theory of module categories over monoidal categories (this is a
straightforward categorization of modules over rings). As applications we show that any
semisimple monoidal…

Fermion condensation and super pivotal categories

- Physics, Mathematics
- 2017

We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion.…

Some unitary representations of Thompson's groups F and T

- Mathematics, Physics
- 2014

In a "naive" attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson's groups T and F for any subfactor. The Thompson group…

Computing data for Levin-Wen with defects

- Computer Science, PhysicsQuantum
- 2020

This work demonstrates how to do many computations for doubled topological phases with defects using generalized tube algebra techniques, and shows all possible point defects, and the fusion and associator data of these.

Clebsch–Gordan and 6j-coefficients for rank 2 quantum groups

- Mathematics, Physics
- 2010

We calculate (q-deformed) Clebsch–Gordan and 6j-coefficients for rank 2 quantum groups. We explain in detail how such calculations are done, which should allow the reader to perform similar…

String-net condensation: A physical mechanism for topological phases

- Physics
- 2005

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''…

A Remark on CFT Realization of Quantum Doubles of Subfactors: Case Index $${ < 4}$$<4

- Mathematics, Physics
- 2015

AbstractIt is well known that the quantum double $${D(N\subset M)}$$D(N⊂M) of a finite depth subfactor $${N\subset M}$$N⊂M, or equivalently the Drinfeld center of the even part fusion category, is a…