Algebraic and Geometric Topology 3 (2003), paper no. 25, pages 719-775.

Near-group categories

Jacob Siehler

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

AMS subject classification. Primary: 18D10.

DOI: 10.2140/agt.2003.3.719

E-print: arXiv:math.QA/0209073

Submitted: 8 November 2002. Accepted: 13 March 2003. Published: 3 August 2003.

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Jacob Siehler
Department of Mathematics, Virginia Tech
Blacksburg, VA 24061-0123, USA

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