We introduce a notion of transitive family of projections in a type II1 factor and prove that there exists (i) a 5 element transitive family in the hyperfinite II1 and (ii) a 12 element free transitive family. We then prove that the group von Neumann algebras of the known infinite free Burnside groups are all type II1 factors. Our investigation of weak-amenability properties of Burnside groups leads us to consider the Connes theory of correspondences. From this investigation we are able to define a new Folner invariant for type II1 factors. We prove a monotonicity result and find a positive lower bound for the free group factor L( F2 ).
","abstract_html":"<p>We introduce a notion of transitive family of projections in a type II1 factor and prove that there exists (i) a 5 element transitive family in the hyperfinite II1 and (ii) a 12 element free transitive family. We then prove that the group von Neumann algebras of the known infinite free Burnside groups are all type II1 factors. Our investigation of weak-amenability properties of Burnside groups leads us to consider the Connes theory of correspondences. From this investigation we are able to define a new Folner invariant for type II1 factors. We prove a monotonicity result and find a positive lower bound for the free group factor L( F2 ).</p>","abstract_has_math":false,"creators":["Bannon, Jon P"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Liming Ge"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-01-01T08:00:00Z","date_published":"2005-01-01T08:00:00Z","updated_at":"2026-07-24T05:22:12Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholars.unh.edu/dissertation/258","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Liming Ge"]},{"key":"dc:creator","label":"Author","values":["Bannon, Jon P"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholars.unh.edu/dissertation/258"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We introduce a notion of transitive family of projections in a type II1 factor and prove that there exists (i) a 5 element transitive family in the hyperfinite II1 and (ii) a 12 element free transitive family. We then prove that the group von Neumann algebras of the known infinite free Burnside groups are all type II1 factors. Our investigation of weak-amenability properties of Burnside groups leads us to consider the Connes theory of correspondences. From this investigation we are able to define a new Folner invariant for type II1 factors. We prove a monotonicity result and find a positive lower bound for the free group factor L( F2 ).
"]},{"key":"dc:title","label":"Title","values":["Burnside factors, amenability defects and transitive families of projections in factors of type II(1)"]}]}],"canonical_facts":{"dc:contributor":["Liming Ge"],"dc:creator":["Bannon, Jon P"],"dc:description.abstract":["We introduce a notion of transitive family of projections in a type II1 factor and prove that there exists (i) a 5 element transitive family in the hyperfinite II1 and (ii) a 12 element free transitive family. We then prove that the group von Neumann algebras of the known infinite free Burnside groups are all type II1 factors. Our investigation of weak-amenability properties of Burnside groups leads us to consider the Connes theory of correspondences. From this investigation we are able to define a new Folner invariant for type II1 factors. We prove a monotonicity result and find a positive lower bound for the free group factor L( F2 ).
"],"dc:identifier":["https://scholars.unh.edu/dissertation/258"],"dc:subject":["Mathematics"],"dc:title":["Burnside factors, amenability defects and transitive families of projections in factors of type II(1)"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T05:22:12Z"}