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Classifying module categories for generalized Temperley–Lieb–Jones ∗-2-categories

Department of Mathematics, University of Puerto Rico (Mayagüez), Call box 9000 Mayagüez, Puerto Rico 00681-9018, Puerto Rico

Department of Mathematics, The Ohio State University, 100 Math Tower 231 West 18th Avenue Columbus OH, 43210-1174, USA

E-mail Address: [email protected]

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and

Roberto Hernández Palomares

http://orcid.org/0000-0002-7647-8444

Department of Mathematics, University of Puerto Rico (Mayagüez), Call box 9000 Mayagüez, Puerto Rico 00681-9018, Puerto Rico

Department of Mathematics, The Ohio State University, 100 Math Tower 231 West 18th Avenue Columbus OH, 43210-1174, USA

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0129167X20500275Cited by:0 (Source: Crossref)

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Generalized Temperley–Lieb–Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker.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 ${Rep(SU}_{q} (2))$ .

Keywords:

AMSC: 18D05, 18D20, 20G42

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