Online Archive of University of Virginia Scholarship
Von Neumann Orbit Equivalence183 views
Author
Wu, Aoran, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Advisors
Hayes, Benjamin, Mathematics, University of Virginia
Abstract
This thesis generalizes the notion of orbit equivalence to the non-commutative setting by introducing a new equivalence relation on groups, which we call von Neumann orbit equivalence (vNOE). This thesis proves the stability of this equivalence relation under taking free products and graph products of groups. To achieve this, von Neumann orbit equivalence of tracial von Neumann algebras is introduced. This thesis shows that two countable discrete groups vNOE if and only if the corresponding group von Neumann algebras are vNOE, and that vNOE of tracial von Neumann algebras is stable under taking free products and graph products of tracial von Neumann algebras.
Degree
PHD (Doctor of Philosophy)
Keywords
Von Neumann orbit equivalence; von Neumann equivalence; free product; graph product
Language
English
Rights
All rights reserved (no additional license for public reuse)
Wu, Aoran. Von Neumann Orbit Equivalence. University of Virginia, Mathematics - Graduate School of Arts and Sciences, PHD (Doctor of Philosophy), 2025-04-30, https://doi.org/10.18130/0wk9-7t61.
