Near-group categories

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

References

Forward citations

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

Volume 3, issue 2 (2003)

Jacob Siehler