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Title page for ETD etd-06152016-134905


Type of Document Dissertation
Author Wen, Chenxu
Author's Email Address chenxu.wen@vanderbilt.edu
URN etd-06152016-134905
Title Amenable Extensions in II1 Factors
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Jesse Peterson Committee Chair
Denis Osin Committee Member
Dietmar Bisch Committee Member
Sokrates Pantelides Committee Member
Vaughan Jones Committee Member
Keywords
  • amenability
  • radial masa
  • free group factor
  • planar algebra
  • cup subalgebra
Date of Defense 2016-04-25
Availability unrestricted
Abstract
Amenability is a fundamental in operator algebras. The classification of von Neumann algebras by Alain Connes is a milestone in the theory. The study of amenable subalgebras in II1 factors has led to many important developments such as the computation of the fundamental groups, strong solidity of free group factors, etc. In this thesis we consider a question about amenable extension in II1 factors, namely, given a diffuse amenable subalgebra in a II1 factor, in how many ways it can be extended to some maximal amenable subalgebra? We give two classes of examples where unique amenable extension results are obtained. The key notion we use is a strengthening of Popa’s asymptotic orthogonality property.
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