Algebraic and Geometric Topology 3 (2003),
paper no. 25, pages 719-775.
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.
Monoidal categories, braided categories
AMS subject classification.
Submitted: 8 November 2002.
Accepted: 13 March 2003.
Published: 3 August 2003.
Notes on file formats
Department of Mathematics, Virginia Tech
Blacksburg, VA 24061-0123, USA
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