Central sequences in the factor associated with Thompson’s group F

Paul Jolissaint

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 4, page 1093-1106
  • ISSN: 0373-0956

Abstract

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We prove that the type II 1 factor L ( F ) generated by the regular representation of F is isomorphic to its tensor product with the hyperfinite type II 1 factor. This implies that the unitary group of L ( F ) is contractible with respect to the topology defined by the natural Hilbertian norm.

How to cite

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Jolissaint, Paul. "Central sequences in the factor associated with Thompson’s group $F$." Annales de l'institut Fourier 48.4 (1998): 1093-1106. <http://eudml.org/doc/75310>.

@article{Jolissaint1998,
abstract = {We prove that the type $\{\rm II\}_\{1\}$ factor $L(F)$ generated by the regular representation of $F$ is isomorphic to its tensor product with the hyperfinite type $\{\rm II\}_\{1\}$ factor. This implies that the unitary group of $L(F)$ is contractible with respect to the topology defined by the natural Hilbertian norm.},
author = {Jolissaint, Paul},
journal = {Annales de l'institut Fourier},
keywords = {crossed products; centrally free actions; central sequences; Connes' classification of injective factors; weak form of amenability},
language = {eng},
number = {4},
pages = {1093-1106},
publisher = {Association des Annales de l'Institut Fourier},
title = {Central sequences in the factor associated with Thompson’s group $F$},
url = {http://eudml.org/doc/75310},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Jolissaint, Paul
TI - Central sequences in the factor associated with Thompson’s group $F$
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 4
SP - 1093
EP - 1106
AB - We prove that the type ${\rm II}_{1}$ factor $L(F)$ generated by the regular representation of $F$ is isomorphic to its tensor product with the hyperfinite type ${\rm II}_{1}$ factor. This implies that the unitary group of $L(F)$ is contractible with respect to the topology defined by the natural Hilbertian norm.
LA - eng
KW - crossed products; centrally free actions; central sequences; Connes' classification of injective factors; weak form of amenability
UR - http://eudml.org/doc/75310
ER -

References

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  10. [10] E.G. EFFROS, Property Γ and inner amenability, Proc. Amer. Math. Soc., 47 (1975), 483-486. Zbl0321.22011MR50 #8100
  11. [11] S.M. GERSTEN, and J.R. STALLINGS (eds), Combinatorial Group Theory and Topology, in Annals of Math. Studies 111, Princeton University Press, 1987. Zbl0611.00010
  12. [12] P. JOLISSAINT, Moyennabilité intérieure du groupe F de Thompson, C.R. Acad. Sci. Paris, Série I, 325 (1997), 61-64. Zbl0883.43003MR98j:20049
  13. [13] D. MCDUFF, Central sequences and the hyperfinite factor, Proc. London Math. Soc., 21 (1970), 443-461. Zbl0204.14902MR43 #6737
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  15. [15] S. POPA and M. TAKESAKI, The topological structure of the unitary and automorphism groups of a factor, Comm. Math. Phys., 155 (1993), 93-101. Zbl0799.46074MR94h:46092

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