Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-Categories
Operator Algebras
2026-01-06 v1 Quantum Algebra
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Generalized Temperley-Lieb-Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker.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)).
Cite
@article{arxiv.1905.00471,
title = {Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-Categories},
author = {Giovanni Ferrer and Roberto Hernandez Palomares},
journal= {arXiv preprint arXiv:1905.00471},
year = {2026}
}
Comments
21 pages