7 papers
Frobenius subalgebra lattices in tensor categories
Mainak Ghosh, Sebastien Palcoux
This paper generalizes Watatani's finiteness theorem for intermediate subfactors to a wide class of monoidal categories. We characterize the sublattices of Frobenius subalgebra pos…
Classification of integral modular data up to rank 13
Max A. Alekseyev, Winfried Bruns, Sebastien Palcoux +1
This paper classifies the modular data of integral modular fusion categories up to rank 13, and integral half-Frobenius fusion rings up to rank 12. We establish that every perfect…
Triangular Prism Equations and Categorification
Zhengwei Liu, Sebastien Palcoux, Yunxiang Ren +1
We introduce the triangular prism equations (TPE) for fusion categories, obtained by evaluating triangular prisms in terms of tetrahedra. Using an oriented graphical calculus, we s…
Exchange relations and Frobenius subalgebras
Mainak Ghosh, Sebastien Palcoux
Bisch and Jones established a bijection between the intermediate subfactors of an irreducible subfactor and certain idempotents satisfying exchange relations. In this paper, we gen…
A new criterion for integral modular categorification
Jingcheng Dong, Sebastien Palcoux
A generalization of an argument due to Etingof-Nikshych-Ostrik yields a highly efficient necessary criterion for integral modular categorification. This criterion allows us to comp…
Classifying integral Grothendieck rings up to rank 5 and beyond
Max A. Alekseyev, Winfried Bruns, Jingcheng Dong +1
In this paper, we define a Grothendieck ring as a fusion ring categorifiable into a fusion category over the complex field. An integral fusion ring is called Drinfeld if all its fo…