Near-group categories

Details Near-group categories Near-group categories

2002-09-07

arxiv.org/abs/math/0209073v2

Algebr. Geom. Topol. 3 (2003) 719-775

Mathematics

Quantum Algebra

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-25.abs.html

Scientific paper

We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Conditions are given for the existence or nonexistence of coherent associative structures for such fusion rules, and an explicit construction of matrix solutions 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.

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