期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 370, 期 2, 页码 719-757出版社
SPRINGER
DOI: 10.1007/s00220-018-3266-x
关键词
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资金
- EPSRC [EP/K032208/1, EP/R014604/1]
- Department of Mathematics of the Ohio University
- Georg-August-Universitat Gottingen
- MIUR Excellence Department Project [CUP E83C18000100006]
- EPSRC [EP/R014604/1, EP/K032208/1] Funding Source: UKRI
In the first part of this paper, we give a newlook at inclusions of von Neumann algebras with finite-dimensional centers and finite Jones' index. The minimal conditional expectation is characterized by means of a canonical state on the relative commutant, that we call the spherical state; the minimal index is neither additive nor multiplicative (it is submultiplicative), contrary to the subfactor case. So we introduce amatrix dimension with the good functorial properties: it is always additive and multiplicative. Theminimal index turns out to be the square of the norm of the matrix dimension, as was known in the multi-matrix inclusion case. In the second part, we show how our results are valid in a purely 2-C*-categorical context, in particular they can be formulated in the framework of Connes' bimodules over von Neumann algebras.
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