A longstanding open question of Connes asks whether every finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras. As of yet, algebras verified to satisfy Connes's embedding property belong to just a few special classes (e.g. amenable algebras and free group factors). In this dissertation we establish Connes's embedding property for von Neumann algebras satisfying Popa's co-amenability condition. Some decomposition properties of finite von Neumann algebras are also investigated.
Chapter 1 reviews von Neumann algebras, completely bounded mappings, conditional expectations, tensor products, crossed products, direct integrals, and Jones basic construction.
Chapter 2 introduces new decompositions of finite von Neumann algebras which we call F-thin, strongly F-thin, and weakly F-thin, etc. We also consider the singly-generated problem, and compute the cohomology in such decompositions of finite von Neumann algebras.
In Chapter 3 we show by estimation of free entropy that free group factors lack the type of decompositions discussed in Chapter 2.
","abstract_html":"<p>A longstanding open question of Connes asks whether every finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras. As of yet, algebras verified to satisfy Connes's embedding property belong to just a few special classes (e.g. amenable algebras and free group factors). In this dissertation we establish Connes's embedding property for von Neumann algebras satisfying Popa's co-amenability condition. Some decomposition properties of finite von Neumann algebras are also investigated.</p><p>Chapter 1 reviews von Neumann algebras, completely bounded mappings, conditional expectations, tensor products, crossed products, direct integrals, and Jones basic construction.</p><p>Chapter 2 introduces new decompositions of finite von Neumann algebras which we call F-thin, strongly F-thin, and weakly F-thin, etc. We also consider the singly-generated problem, and compute the cohomology in such decompositions of finite von Neumann algebras.</p><p>In Chapter 3 we show by estimation of free entropy that free group factors lack the type of decompositions discussed in Chapter 2.</p>","abstract_has_math":false,"creators":["Wu, Jinsong"],"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":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T05:22:36Z","subjects":["Mathematics","Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholars.unh.edu/dissertation/630","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":["Wu, Jinsong"]}]},{"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","Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholars.unh.edu/dissertation/630"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A longstanding open question of Connes asks whether every finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras. As of yet, algebras verified to satisfy Connes's embedding property belong to just a few special classes (e.g. amenable algebras and free group factors). In this dissertation we establish Connes's embedding property for von Neumann algebras satisfying Popa's co-amenability condition. Some decomposition properties of finite von Neumann algebras are also investigated.
Chapter 1 reviews von Neumann algebras, completely bounded mappings, conditional expectations, tensor products, crossed products, direct integrals, and Jones basic construction.
Chapter 2 introduces new decompositions of finite von Neumann algebras which we call F-thin, strongly F-thin, and weakly F-thin, etc. We also consider the singly-generated problem, and compute the cohomology in such decompositions of finite von Neumann algebras.
In Chapter 3 we show by estimation of free entropy that free group factors lack the type of decompositions discussed in Chapter 2.
"]},{"key":"dc:title","label":"Title","values":["On decompositions and Connes's embedding problem of finite von Neumann algebras"]}]}],"canonical_facts":{"dc:contributor":["Liming Ge"],"dc:creator":["Wu, Jinsong"],"dc:description.abstract":["A longstanding open question of Connes asks whether every finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras. As of yet, algebras verified to satisfy Connes's embedding property belong to just a few special classes (e.g. amenable algebras and free group factors). In this dissertation we establish Connes's embedding property for von Neumann algebras satisfying Popa's co-amenability condition. Some decomposition properties of finite von Neumann algebras are also investigated.
Chapter 1 reviews von Neumann algebras, completely bounded mappings, conditional expectations, tensor products, crossed products, direct integrals, and Jones basic construction.
Chapter 2 introduces new decompositions of finite von Neumann algebras which we call F-thin, strongly F-thin, and weakly F-thin, etc. We also consider the singly-generated problem, and compute the cohomology in such decompositions of finite von Neumann algebras.
In Chapter 3 we show by estimation of free entropy that free group factors lack the type of decompositions discussed in Chapter 2.
"],"dc:identifier":["https://scholars.unh.edu/dissertation/630"],"dc:subject":["Mathematics","Applied Mathematics"],"dc:title":["On decompositions and Connes's embedding problem of finite von Neumann algebras"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T05:22:36Z"}