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

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

Generalized Temperley-Lieb-Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker.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 bigrad...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2019-05
Hauptverfasser: Ferrer, Giovanni, Roberto Hernandez Palomares
Format: Artikel
Sprache:eng
Schlagworte:
Categories
Classification
Graphs
Hilbert space
Modules
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Ferrer, Giovanni
Roberto Hernandez Palomares
description Generalized Temperley-Lieb-Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker.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)).
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2219318988</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2219318988</sourcerecordid><originalsourceid>FETCH-proquest_journals_22193189883</originalsourceid><addsrcrecordid>eNqNiz0LwjAUAIMgWLT_IeAcaF-spnPxA1FwcC-RvpaUmNS8dqi_3g6Cq9MNdzdjEUiZCrUBWLCYqE2SBLY7yDIZsVthNZGpR-MafvXVYJEXusfGB4PEax_4ER0Gbc0bK37HZ4fB4iguBh_i7N0UCRC_ZcXmtbaE8ZdLtj7s78VJdMG_BqS-bP0Q3KRKgDSXqcqVkv9VH0jnPrI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2219318988</pqid></control><display><type>article</type><title>Classifying Module Categories for Generalized Temperley-Lieb-Jones -2-Categories</title><source>Free E- Journals</source><creator>Ferrer, Giovanni ; Roberto Hernandez Palomares</creator><creatorcontrib>Ferrer, Giovanni ; Roberto Hernandez Palomares</creatorcontrib><description>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)).</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Categories ; Classification ; Graphs ; Hilbert space ; Modules</subject><ispartof>arXiv.org, 2019-05</ispartof><rights>2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>776,780</link.rule.ids></links><search><creatorcontrib>Ferrer, Giovanni</creatorcontrib><creatorcontrib>Roberto Hernandez Palomares</creatorcontrib><title>Classifying Module Categories for Generalized Temperley-Lieb-Jones -2-Categories</title><title>arXiv.org</title><description>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)).</description><subject>Categories</subject><subject>Classification</subject><subject>Graphs</subject><subject>Hilbert space</subject><subject>Modules</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNiz0LwjAUAIMgWLT_IeAcaF-spnPxA1FwcC-RvpaUmNS8dqi_3g6Cq9MNdzdjEUiZCrUBWLCYqE2SBLY7yDIZsVthNZGpR-MafvXVYJEXusfGB4PEax_4ER0Gbc0bK37HZ4fB4iguBh_i7N0UCRC_ZcXmtbaE8ZdLtj7s78VJdMG_BqS-bP0Q3KRKgDSXqcqVkv9VH0jnPrI</recordid><startdate>20190501</startdate><enddate>20190501</enddate><creator>Ferrer, Giovanni</creator><creator>Roberto Hernandez Palomares</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20190501</creationdate><title>Classifying Module Categories for Generalized Temperley-Lieb-Jones -2-Categories</title><author>Ferrer, Giovanni ; Roberto Hernandez Palomares</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_22193189883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Categories</topic><topic>Classification</topic><topic>Graphs</topic><topic>Hilbert space</topic><topic>Modules</topic><toplevel>online_resources</toplevel><creatorcontrib>Ferrer, Giovanni</creatorcontrib><creatorcontrib>Roberto Hernandez Palomares</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ferrer, Giovanni</au><au>Roberto Hernandez Palomares</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Classifying Module Categories for Generalized Temperley-Lieb-Jones -2-Categories</atitle><jtitle>arXiv.org</jtitle><date>2019-05-01</date><risdate>2019</risdate><eissn>2331-8422</eissn><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)).</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2019-05
issn 2331-8422
language eng
recordid cdi_proquest_journals_2219318988
source Free E- Journals
subjects Categories
Classification
Graphs
Hilbert space
Modules
title Classifying Module Categories for Generalized Temperley-Lieb-Jones -2-Categories
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-26T22%3A44%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Classifying%20Module%20Categories%20for%20Generalized%20Temperley-Lieb-Jones%20-2-Categories&rft.jtitle=arXiv.org&rft.au=Ferrer,%20Giovanni&rft.date=2019-05-01&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2219318988%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2219318988&rft_id=info:pmid/&rfr_iscdi=true