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Abstract
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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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Keywords
monoidal categories, braided categories
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Mathematical Subject Classification 2000
Primary: 18D10
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Publication
Received: 8 November 2002
Accepted: 13 March 2003
Published: 3 August 2003
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