Canonical extension of endomorphisms of type III factors

Details Canonical extension of endomorphisms of type III factors Canonical extension of endomorphisms of type III factors

2001-04-24

arxiv.org/abs/math/0104228v1

Mathematics

Operator Algebras

Scientific paper

We extend the notion of the canonical extension of automorphisms of type III factors to the case of endomorphisms with finite statistical dimensions. Following the automorphism case, we introduce two notions for endomorphisms of type III factors: modular endomorphisms and Connes-Takesaki modules. Several applications to compact groups of automorphisms and subfactors of type III factors are given from the viewpoint of ergodic theory.

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