• Corpus ID: 236881562

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

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



Pseudo-unitary non-self-dual fusion categories of rank 4

volume 441 of Contemp

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

Tetrahedral symmetry of 6j-symbols in fusion categories

Generalized string-net models: A thorough exposition

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

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,


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

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

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

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