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arXiv · 1905.00471

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

Giovanni Ferrer·Roberto Hernandez Palomares
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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Generalized Temperley-Lieb-Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker.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)).

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Giovanni Ferrer, Roberto Hernandez Palomares. 2019-05-01. Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-Categories. https://doi.org/10.1142/s0129167x20500275

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