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