Traces on ideals in pivotal categories
Nathan Geer, Bertrand Patureau-Mirand, Alexis Virelizier
TL;DR
This paper extends the concept of ambidextrous traces to pivotal categories, enabling the construction of invariants for colored spherical graphs and contributing to the theory of modified 6j-symbols.
Contribution
It generalizes ambidextrous traces to pivotal categories, facilitating new invariants for spherical graphs and advancing the understanding of modified 6j-symbols.
Findings
Defined ambidextrous traces in pivotal categories
Constructed invariants of colored spherical graphs
Linked traces to modified 6j-symbols
Abstract
We extend the notion of an ambidextrous trace on an ideal (developed by the first two authors) to the setting of a pivotal category. We show that under some conditions, these traces lead to invariants of colored spherical graphs (and so to modified 6j-symbols).
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