Near-group categories

By Jacob A. Siehler. 2002

53 citations recorded by the source corpus.

We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Con- ditions are given for the existence or nonexistence of coherent associative structures for such fusion rules, and an explicit construction of matrix so- lutions to the pentagon equations in the cases where we establish existence. Many of these also support (braided) commutative and tortile structures and we indicate when this is possible. Small examples are presented in detail. AMS Classication 18D10

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cc88627b838ebd078c95e55a7d823a20f8511230