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2003 Near-group categories
Jacob Siehler
Algebr. Geom. Topol. 3(2): 719-775 (2003). DOI: 10.2140/agt.2003.3.719

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.

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Jacob Siehler. "Near-group categories." Algebr. Geom. Topol. 3 (2) 719 - 775, 2003. https://doi.org/10.2140/agt.2003.3.719

Information

Received: 8 November 2002; Accepted: 13 March 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1033.18004
MathSciNet: MR1997336
Digital Object Identifier: 10.2140/agt.2003.3.719

Subjects:
Primary: 18D10

Rights: Copyright © 2003 Mathematical Sciences Publishers

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