Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Factors from trees


Authors: Jacqui Ramagge and Guyan Robertson
Journal: Proc. Amer. Math. Soc. 125 (1997), 2051-2055
MSC (1991): Primary 46L10
MathSciNet review: 1377004
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We construct factors of type $\mathrm {III}_{1/n}$ for $n\in {\Bbb N}, n\geq 2$, from group actions on homogeneous trees and their boundaries. Our result is a discrete analogue of a result of R.J Spatzier, where the hyperfinite factor of type $\mathrm {III}_{1}$ is constructed from a group action on the boundary of the universal cover of a manifold.


References [Enhancements On Off] (What's this?)

  • [A] S. Adams. Boundary amenability for word hyperbolic groups and an application to smooth dynamics of simple groups. Topology 33 (1994), 765-783.
  • [CKW] D. I. Cartwright, V. A. Kaĭmanovich, and W. Woess, Random walks on the affine group of local fields and of homogeneous trees, Ann. Inst. Fourier (Grenoble) 44 (1994), no. 4, 1243–1288 (English, with English and French summaries). MR 1306556
  • [C1] Alain Connes, Une classification des facteurs de type 𝐼𝐼𝐼, Ann. Sci. École Norm. Sup. (4) 6 (1973), 133–252 (French). MR 0341115
  • [C2] A. Connes, On the classification of von Neumann algebras and their automorphisms, Symposia Mathematica, Vol. XX (Convegno sulle Algebre 𝐶* e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria 𝐾, INDAM, Rome, 1975) Academic Press, London, 1976, pp. 435–478. MR 0450988
  • [FTN] Alessandro Figà-Talamanca and Claudio Nebbia, Harmonic analysis and representation theory for groups acting on homogeneous trees, London Mathematical Society Lecture Note Series, vol. 162, Cambridge University Press, Cambridge, 1991. MR 1152801
  • [HO] T. Hamachi and M. Osikawa, Ergodic Groups Acting of Automorphisms and Krieger's Theorems, Seminar on Mathematical Sciences No. 3, Keio University, Japan, 1981.
  • [PS] C. Pensavalle and T. Steger, Tensor products and anisotropic principal series representations for free groups, Pac. J. Math. 173 (1996), 181-202.
  • [S] R. J. Spatzier, An example of an amenable action from geometry, Ergodic Theory Dynam. Systems 7 (1987), no. 2, 289–293. MR 896799, 10.1017/S0143385700004016
  • [Sp1] John S. Spielberg, Diagonal states on 𝑂₂, Pacific J. Math. 144 (1990), no. 2, 361–382. MR 1061326
  • [Sp2] John Spielberg, Free-product groups, Cuntz-Krieger algebras, and covariant maps, Internat. J. Math. 2 (1991), no. 4, 457–476. MR 1113572, 10.1142/S0129167X91000260

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L10

Retrieve articles in all journals with MSC (1991): 46L10


Additional Information

Jacqui Ramagge
Affiliation: Department of Mathematics, University of Newcastle, Callaghan, New South Wales 2308, Australia
Email: jacqui@maths.newcastle.edu.au

Guyan Robertson
Affiliation: Department of Mathematics, University of Newcastle, Callaghan, New South Wales 2308, Australia
Email: guyan@maths.newcastle.edu.au

DOI: https://doi.org/10.1090/S0002-9939-97-03818-5
Received by editor(s): January 26, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society