Dualizability and index of subfactors

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2011-10-25 DOI:10.4171/QT/53

A. Bartels, Christopher L. Douglas, A. Henriques

引用次数: 50

Abstract

In this paper, we develop the theory of bimodules over von Neumann algebras, with an emphasis on categorical aspects. We clarify the relationship between dualizability and finite index. We also show that, for von Neumann algebras with finite dimensional centers, the Haagerup L 2 -space and Connes fusion are functorial with respect to homor- phisms of finite index. Along the way, we describe a string diagram notation for maps between bimodules that are not necessarily bilinear.

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子因子的可偶性与索引

在本文中，我们发展了von Neumann代数上的双模理论，重点讨论了范畴方面。阐明了可偶性与有限指数之间的关系。我们还证明了对于具有有限维中心的von Neumann代数，Haagerup l2空间和cones融合对于有限指标的同态是泛函的。在此过程中，我们描述了不一定是双线性的双模之间映射的字符串图符号。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.