# Classification of $\mathbb{Z}/2\mathbb{Z}$-quadratic unitary fusion categories

@inproceedings{EDIEMICHELL2021ClassificationO, title={Classification of \$\mathbb\{Z\}/2\mathbb\{Z\}\$-quadratic unitary fusion categories}, author={Cain EDIE-MICHELL and Masaki Izumi and David Penneys}, year={2021} }

A unitary fusion category is called Z/2Z-quadratic if it has a Z/2Z group of invertible objects and one other orbit of simple objects under the action of this group. We give a complete classification of Z/2Z-quadratic unitary fusion categories. The main tools for this classification are skein theory, a generalization of Ostrik’s results on formal codegrees to analyze the induction of the group elements to the center, and a computation similar to Larson’s rank-finiteness bound for Z/3Z-near…

## References

SHOWING 1-10 OF 53 REFERENCES

### volume 441 of Contemp

- Math., pages 63–90. Amer. Math. Soc., Providence, RI,
- 2007

### Tetrahedral symmetry of 6j-symbols in fusion categories

- MathematicsJournal of Pure and Applied Algebra
- 2022

### Generalized string-net models: A thorough exposition

- Computer Science
- 2021

This paper provides a more detailed discussion of ground state wave functions, Hamiltonians, and minimal self-consistency conditions for generalized string-net models than what exists in the previous literature.

### Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six

- MathematicsLetters in Mathematical Physics
- 2022

This paper classifies Grothendieck rings of complex fusion categories of multiplicity one up to rank six, as an application of a localization approach of the Pentagon Equation and some new criteria,…

### PIVOTAL FUSION CATEGORIES OF RANK 3

- Mathematics
- 2014

We classify all fusion categories of rank 3 that admit a pivotal structure over an algebraically closed field of characteristic zero. Also in the Appendix (joint with D. Nikshych) we give some…

### On a q-Analogue of the McKay Correspondence and the ADE Classification of sl̂2 Conformal Field Theories

- Mathematics
- 2002

Abstract The goal of this paper is to give a category theory based definition and classification of “finite subgroups in Uq( s l 2)” where q=eπi/l is a root of unity. We propose a definition of such…

### Quantum groups and subfactors of type B, C, and D

- Mathematics
- 1990

The main object of this paper is the study of a sequence of finite dimensional algebras, depending on 2 parameters, which appear in connection with the Kauffman link invariant and with Drinfeld's and…

### Tensor Categories with Fusion Rules of Self-Duality for Finite Abelian Groups

- Mathematics
- 1998

Abstract Semisimple tensor categories with fusion rules of self-duality for finite abelian groups are classified. As an application, we prove that the Tannaka duals of the dihedral and the quaternion…