Rigid C*-tensor categories of bimodules over interpolated free group factors

Abstract

Given a countably generated rigid C*-tensor category ${\sf C}$C, we construct a planar algebra P• whose category of projections ${\sf Pro}$Pro is equivalent to ${\sf C}$C. From P•, we use methods of Guionnet-Jones-Shlyakhtenko-Walker to construct a rigid C*-tensor category ${\sf Bim}$Bim whose objects are bifinite bimodules over an interpolated free group factor, and we show ${\sf Bim}$Bim is equivalent to ${\sf Pro}$Pro. We use these constructions to show ${\sf C}$C is equivalent to a category of bifinite bimodules over $L(\mathbb {F}_\infty )$L(F∞).

Document Details

Document Type
Pub Defense Publication
Publication Date
Dec 01, 2012
Source ID
10.1063/1.4769178

Entities

People

  • Arnaud Brothier
  • David Penneys
  • Michael Hartglass

Organizations

  • Defense Advanced Research Projects Agency
  • National Science Foundation
  • University of California
  • University of Toronto

Tags

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.
  • Quantum Chemistry