Hostname: page-component-7d684dbfc8-7nm9g Total loading time: 0 Render date: 2023-09-29T10:53:03.126Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "coreDisableSocialShare": false, "coreDisableEcommerceForArticlePurchase": false, "coreDisableEcommerceForBookPurchase": false, "coreDisableEcommerceForElementPurchase": false, "coreUseNewShare": true, "useRatesEcommerce": true } hasContentIssue false

One-Parameter Automorphism Groups of the Injective Factor of Type II1 With Connes Spectrum Zero

Published online by Cambridge University Press:  20 November 2018

Yasuyuki Kawahigashi*
Department of Mathematics, Faculty of Science University of Tokyo, Hongo, Tokyo, 113, Japan
Rights & Permissions [Opens in a new window]


Core share and HTML view are not possible as this article does not have html content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct a one-parameter automorphism group of the injective type II1 factor with Connes spectrum ﹛0﹜ which is not stably conjugate to an infinite tensor product action. We construct a countable family of one-parameter automorphism groups of the injective type II1 factor such that all are stably conjugate but no two are cocycle conjugate.


Research Article
Copyright © Canadian Mathematical Society 1991


1. Araki, H. & Woods, E.J., A classification of factors, Publ. RIMS Kyoto Univ. Ser. A 3(1968), 51130.Google Scholar
2. Christensen, E., Subalgebras of a finite algebra, Math. Ann. 243(1979), 1729.Google Scholar
3. Connes, A., Outer conjugacy classes of automorphisms of factors, Ann. Sci. École Norm. Sup. 8(1975), 383–119.Google Scholar
4. Connes, A. & Woods, E.J., A construction of approximately finite-dimensional non-ITPFI factors, Canad. Math. Bull. 23(1980), 227230.Google Scholar
5. Harris, T.E. & Robins, H., Ergodic theory of Markov chains admitting an infinite invariant measure, Proc. Nat. Acad. Sci. U.S.A. 39(1953), 860864.Google Scholar
6. Jones, V.F.R., Index for subfactors, Invent. Math. 72(1983), 115.Google Scholar
7. Jones, V.F.R., Prime actions of compact abelian groups on the hyperfinite type II1 factor, J. Operator Theory 9(1983), 81186.Google Scholar
8. Jones, V.F.R. & Takesaki, M., Actions of compact abelian groups on semifinite injective factors, Acta Math. 153(1984), 213258.Google Scholar
9. Kawahigashi, Y., Centrally ergodic one-parameter automorphism groups on semifinite injective von Neumann algebras, Math. Scand.64(1989),285289.Google Scholar
10. Kawahigashi, Y., One-parameter automorphism groups of the hyperfinite type II1 factor, (to appear in J. Operator Th.).Google Scholar
11. Kawahigashi, Y., One-parameter automorphism groups of the injective II1 factor arising from the irrational rotation C*-algebra, Amer. J. Math. 112(1990),499524.Google Scholar
12. Ocneanu, A., Actions of discrete amenable groups on factors,” Lecture Notes in Math. No. 1138, Springer, Berlin, 1985.Google Scholar
13. Olesen, D., Pedersen, G.K. & Takesaki, M., Ergodic actions of compact abelian groups, J. Operator Theory 3(1980), 237269.Google Scholar
14. Paschke, W., Inner product modules arising from compact automorphism groups on von Neumann algebras, Trans. Amer. Math. Soc. 224(1976), 87102.Google Scholar