{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/99314"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/99314","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic","abstract":"DSpace SAF Submission Ingestion Package generated from Vireo submission #11707 on 2018-03-13 at 10:08:13","abstract_html":"DSpace SAF Submission Ingestion Package generated from Vireo submission #11707 on 2018-03-13 at 10:08:13","abstract_has_math":false,"creators":["Tian, Hongfei"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Haboush, William J.","Bergvelt, Maarten J.","Yong, Alexander","Nevins, Thomas A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-03-13T15:45:10Z","date_published":"2018-03-13T15:45:10Z","updated_at":"2026-07-22T22:24:37Z","subjects":["Representation theory","Positive characteristic","Invariant differential operators","Semisimple center"],"languages":["en"],"rights":["Copyright 2017 Hongfei Tian"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/99314","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Haboush, William J.","Bergvelt, Maarten J.","Yong, Alexander","Nevins, Thomas A."]},{"key":"dc:creator","label":"Author","values":["Tian, Hongfei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-03-13T15:45:10Z","2017-10-30","2017-12"]},{"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":["Representation theory","Positive characteristic","Invariant differential operators","Semisimple center"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Hongfei Tian"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/99314"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["DSpace SAF Submission Ingestion Package generated from Vireo submission #11707 on 2018-03-13 at 10:08:13","In this thesis we prove the existence of Jordan Decomposition in $D_{G/k}$, the ring of invariant differential operators on a semisimple algebraic group over a field of positive characteristic, and its corollaries. In particular, we define the semisimple center of $D_{G/k}$, denoted by $Z_s(D_{G/k})$, as the set of semisimple elements of its center. Then we show that if $G$ is connected, the semisimple center $Z_s(D_{G/k})$ contains $Z_s(D_{G/k}^{(\\nu)})$ for any positive interger $\\nu$, where $Z_s(D_{G/k}^{(\\nu)})$ is the ring of invariant differential operators on a Frobenius kernel derived from $G$.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-03-13 without embargo terms","The student, Hongfei Tian, accepted the attached license on 2017-10-26 at 14:48.","The student, Hongfei Tian, submitted this Dissertation for approval on 2017-10-26 at 14:49.","This Dissertation was approved for publication on 2017-10-30 at 14:06.","Made available in DSpace on 2018-03-13T15:45:10Z (GMT). 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In particular, we define the semisimple center of $D_{G/k}$, denoted by $Z_s(D_{G/k})$, as the set of semisimple elements of its center. Then we show that if $G$ is connected, the semisimple center $Z_s(D_{G/k})$ contains $Z_s(D_{G/k}^{(\\nu)})$ for any positive interger $\\nu$, where $Z_s(D_{G/k}^{(\\nu)})$ is the ring of invariant differential operators on a Frobenius kernel derived from $G$.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-03-13 without embargo terms","The student, Hongfei Tian, accepted the attached license on 2017-10-26 at 14:48.","The student, Hongfei Tian, submitted this Dissertation for approval on 2017-10-26 at 14:49.","This Dissertation was approved for publication on 2017-10-30 at 14:06.","Made available in DSpace on 2018-03-13T15:45:10Z (GMT). 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