Fusion categories of rank 2

By V. Ostrik. 2002

111 citations recorded by the source corpus.

We classify semisimple rigid monoidal categories with two isomorphism classes of simple objects over the field of complex numbers. In the appendix written by P.Etingof it is proved that the number of semisimple Hopf algebras with a given finite number of irreducible representations is finite.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dbb1c678f500e4818f76a2beead61049a1adb80b

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In Algebra and Number Theory

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Topological defect lines and renormalization group flows in two dimensions (2018, methodology): “eck ring fusion ring Table 1: Summary of the relations between fusion category and TDLs. 3.1 On fusion categories of small ranks Fusion categories containing only two simple objects were classied in [67]. In the TDL language, there is only one nontrivial TDL X in addition to the trivial line I, with”
On finite symmetries and their gauging in two dimensions (2017, unknown): “Ostrik also classified all possible symmetry categories with three simple objects [26].”
Near-group categories (2002, background): “the ground ring R is not equal to 2. Then, in the minimal case |G| = 1, the near-group fusion rule (G,k) does not admit a monoidal structure if k≡ 2 or 3 mod 4 Remark A stronger result is obtained in [O] for the case where the ground ring has characteristic zero, but the present proof works also for”
Tensor categories: a selective guided tour (2008, background): “• For fusion categories, there are a number of classification results in the case of low rank (number of simple objects) (Ostrik: fusion categories of rank 2 [224], braided fusion categories of rank 3 [225]) or special dimensions, like p or pq (Etingof/Gelaki/Ostrik [82]).”