Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-Categories

Abstract

Generalized Temperley-Lieb-Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker. We introduce unitary modules for these generalized TLJ 2-categories as strong *-pseudofunctors into the *-2-category of row-finite separable bigraded Hilbert spaces. We classify these modules up to *-equivalence in terms of weighted bi-directed fair and balanced graphs in the spirit of Yamagami's classification of fiber functors on TLJ categories and DeCommer and Yamashita's classification of unitary modules for Rep(SUq(2)).

21 pages

References in corpus (3)

• Operator algebras in rigid C*-tensor categories
• Fiber Functors on Temperley-Lieb Categories
• Module categories over representations of $S{L}_q(2)$ and graphs