Quantum Topology


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Volume 4, Issue 1, 2013, pp. 91–124
DOI: 10.4171/QT/36

Published online: 2012-11-24

Traces on ideals in pivotal categories

Nathan Geer[1], Bertrand Patureau-Mirand[2] and Alexis Virelizier[3]

(1) Utah State University, Logan, USA
(2) Université de Bretagne-Sud, Vannes, France
(3) Université de Montpellier II, France

We construct invariants of $\mathcal{C}$-colored spherical graphs from traces on ideals in a pivotal category $\mathcal{C}$. Then we provide a systematic approach to defining such traces from ambidextrous and spherical traces on a class of objects of $\mathcal{C}$. This extends the notion of an ambidextrous object of a braided category given by the first two authors in a previous work.

Keywords: Pivotal category, trace, ideal, ambidextrous

Geer Nathan, Patureau-Mirand Bertrand, Virelizier Alexis: Traces on ideals in pivotal categories. Quantum Topol. 4 (2013), 91-124. doi: 10.4171/QT/36