{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/124587"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/124587","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Coend elements of a Hopf algebra in a braided rigid monoidal category","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01","abstract_has_math":false,"creators":["Nguyen, Anh Tuong"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Walton, Chelsea","Dodd, Christopher","Rezk, Charles","Berwick-Evans, Daniel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-05","date_published":"2024-05","updated_at":"2026-07-22T22:25:02Z","subjects":["Braided Hopf Algebra","Coend","Modular Tensor Category","Pivotal Element","Ribbon Element"],"languages":["en","eng"],"rights":["Copyright 2024 Anh Tuong Nguyen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/124587","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Walton, Chelsea","Dodd, Christopher","Rezk, Charles","Berwick-Evans, Daniel"]},{"key":"dc:creator","label":"Author","values":["Nguyen, Anh Tuong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-05","2024-04-29"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Braided Hopf Algebra","Coend","Modular Tensor Category","Pivotal Element","Ribbon Element"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2024 Anh Tuong Nguyen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/124587"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01","The student, Anh Tuong Nguyen, accepted the attached license on 2024-04-26 at 13:24.","The student, Anh Tuong Nguyen, submitted this Dissertation for approval on 2024-04-26 at 14:04.","This Dissertation was approved for publication on 2024-04-29 at 13:10.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20659 on 2024-09-16 at 00:44:48","Let H be a Hopf algebra in a braided rigid monoidal category V admitting a coend C. We define a “coend element” of H to be a morphism from C to H. We then study certain coend elements of H, which generalize important elements (e.g., pivotal and ribbon elements) of a finite dimensional Hopf algebra over a field. This builds on prior work of Bruguieres and Virelizier on elements of Hopf monads and R-matrices of braided Hopf algebras. As a consequence, we provide another description for pivotal and ribbon structures on the category of H-modules."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Coend elements of a Hopf algebra in a braided rigid monoidal category"]}]}],"canonical_facts":{"dc:contributor":["Walton, Chelsea","Dodd, Christopher","Rezk, Charles","Berwick-Evans, Daniel"],"dc:creator":["Nguyen, Anh Tuong"],"dc:date":["2024-05","2024-04-29"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01","The student, Anh Tuong Nguyen, accepted the attached license on 2024-04-26 at 13:24.","The student, Anh Tuong Nguyen, submitted this Dissertation for approval on 2024-04-26 at 14:04.","This Dissertation was approved for publication on 2024-04-29 at 13:10.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20659 on 2024-09-16 at 00:44:48","Let H be a Hopf algebra in a braided rigid monoidal category V admitting a coend C. We define a “coend element” of H to be a morphism from C to H. We then study certain coend elements of H, which generalize important elements (e.g., pivotal and ribbon elements) of a finite dimensional Hopf algebra over a field. This builds on prior work of Bruguieres and Virelizier on elements of Hopf monads and R-matrices of braided Hopf algebras. As a consequence, we provide another description for pivotal and ribbon structures on the category of H-modules."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/124587"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Anh Tuong Nguyen"],"dc:subject":["Braided Hopf Algebra","Coend","Modular Tensor Category","Pivotal Element","Ribbon Element"],"dc:title":["Coend elements of a Hopf algebra in a braided rigid monoidal category"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:02Z"}