2002/09/30 by Jacob Siehler
Mathematics · #math.QA #msc:18D10
paper · pdf · doi:10.2140/agt.2003.3.719
published as Algebr. Geom. Topol. 3 (2003) 719-775 · Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-25.abs.html
arxiv created 2003/08/27 · arxiv updated 2014/09/30
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.