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Jacob Siehler

Algebraic & Geometric Topology 3 (2003) 719–775

arXiv: math.QA/0209073

Abstract

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.

Keywords
monoidal categories, braided categories
Mathematical Subject Classification 2000
Primary: 18D10
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Publication
Received: 8 November 2002
Accepted: 13 March 2003
Published: 3 August 2003
Authors
Jacob Siehler
Department of Mathematics
Virginia Tech
Blacksburg, VA 24061-0123
USA