{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/9033"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/9033","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Decomposition of Certain Representations Into A Direct Sum of Indecomposable Representations","abstract":"Representations of quivers and posets are produced by persistent homology. It is possible to decompose such representations into direct sums of indecomposable representations. The indecomposable representations of quivers and posets that arise from one dimensional persistent homology are well understood. However, the same is not true for multidimensional persistent homology. This thesis finds such a list of indecomposable representations for a very simple case of a poset that can arise from multidimensional persistent homology, and proves that it is possible to decompose a representation of such a poset into a direct sum of these indecomposables.","abstract_html":"Representations of quivers and posets are produced by persistent homology. It is possible to decompose such representations into direct sums of indecomposable representations. The indecomposable representations of quivers and posets that arise from one dimensional persistent homology are well understood. However, the same is not true for multidimensional persistent homology. This thesis finds such a list of indecomposable representations for a very simple case of a poset that can arise from multidimensional persistent homology, and proves that it is possible to decompose a representation of such a poset into a direct sum of these indecomposables.","abstract_has_math":false,"creators":["Zhang, Yihui"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Science (MSc)","degree_level":"Master's","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Stanley, Donald"],"committee_chairs":[],"committee_members":["Herman, Allen","Frankland, Martin"],"year":2019,"date_issued":"2019-04","date_published":"2019-04","updated_at":"2026-07-24T04:03:38Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4443"],"render_values":[{"text":"https://doi.org/10.82465/4443","href":"https://doi.org/10.82465/4443","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/9033","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Stanley, Donald"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Herman, Allen","Frankland, Martin"]},{"key":"dc:creator","label":"Author","values":["Zhang, Yihui"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-11-21T17:49:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-11-21T17:49:38Z"]},{"key":"dc:date.issued","label":"Date","values":["2019-04"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4443"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/9033"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics, University of Regina. iv, 98 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["Representations of quivers and posets are produced by persistent homology. It is possible to decompose such representations into direct sums of indecomposable representations. The indecomposable representations of quivers and posets that arise from one dimensional persistent homology are well understood. However, the same is not true for multidimensional persistent homology. This thesis finds such a list of indecomposable representations for a very simple case of a poset that can arise from multidimensional persistent homology, and proves that it is possible to decompose a representation of such a poset into a direct sum of these indecomposables."]},{"key":"dc:title","label":"Title","values":["Decomposition of Certain Representations Into A Direct Sum of Indecomposable Representations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Stanley, Donald"],"dc:contributor.committeemember":["Herman, Allen","Frankland, Martin"],"dc:creator":["Zhang, Yihui"],"dc:date.accessioned":["2019-11-21T17:49:38Z"],"dc:date.available":["2019-11-21T17:49:38Z"],"dc:date.issued":["2019-04"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics, University of Regina. iv, 98 p."],"dc:description.abstract":["Representations of quivers and posets are produced by persistent homology. It is possible to decompose such representations into direct sums of indecomposable representations. The indecomposable representations of quivers and posets that arise from one dimensional persistent homology are well understood. However, the same is not true for multidimensional persistent homology. This thesis finds such a list of indecomposable representations for a very simple case of a poset that can arise from multidimensional persistent homology, and proves that it is possible to decompose a representation of such a poset into a direct sum of these indecomposables."],"dc:identifier.doi":["https://doi.org/10.82465/4443"],"dc:identifier.uri":["https://hdl.handle.net/10294/9033"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Decomposition of Certain Representations Into A Direct Sum of Indecomposable Representations"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:38Z"}