Abstract
We describe the structure of (finite-index) inclusion of type III factors based on analysis of involved flows of weights. Roughly speaking, a type HI index theory splits into a “purely type III” index theory and an (essentially) type II index theory. The factor flows constructed in [1] serve as the complete invariant for the former in the AFD case while the latter can be analyzed by paragroups or quantized groups (as announced in [7]). Therefore, classification of subfactors in an AFD type III factor reduces to classification of factor flows and an “equivariant” paragroup theory.
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References
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© 1991 Springer Science+Business Media New York
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Kosaki, H. (1991). Index Theory for Type III Factors. In: Araki, H., Kadison, R.V. (eds) Mappings of Operator Algebras. Progress in Mathematics, vol 84. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0453-4_11
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DOI: https://doi.org/10.1007/978-1-4612-0453-4_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6767-6
Online ISBN: 978-1-4612-0453-4
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