Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T06:25:54.121Z Has data issue: false hasContentIssue false
  • English
  • Français

MEASURE-MULTIPLICITY OF THE LAPLACIAN MASA

Published online by Cambridge University Press:  02 August 2012

KEN DYKEMA  and
KUNAL MUKHERJEE
KEN DYKEMA
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA e-mail: kdykema@math.tamu.edu
KUNAL MUKHERJEE
Affiliation:
Institute of Mathematical Sciences, C.I.T Campus, Taramani, Chennai 600113, Tamil Nadu, India e-mail: kunal@imsc.res.in
Rights & Permissions [Opens in a new window]

Abstract

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

It is shown that for the Laplacian masa in the free group factors, the orthocomplement of the associated Jones' projection is an infinite direct sum of coarse bimodules.

Keywords

46L10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 2 , May 2013 , pp. 285 - 292
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Cameron, J., Fang, J. and Mukherjee, K., Mixing and weak mixing abelian subalgebras of type II1 factors (2011), preprint.Google Scholar
2.Cameron, J., Fang, J., Ravichandran, M. and White, S., The radial masa in a free group factor is maximal injective, J. Lond. Math. Soc. 82 (2) (2010), 787–809.CrossRefGoogle Scholar
3.Cohen, J. M., Operator norms on free groups, Boll. Un. Mat. Ital. B 1 (6) (1982), 1055–1065.Google Scholar
4.Dixmier, J., Sous–anneaux abeliens maximaux dans les facteurs de type fini, Ann. Math. 59 (2) (1954), 279–286.Google Scholar
5.Dykema, K., Sinclair, A. M. and Smith, R. R., Values of the Pukanszky invariant in free group factors and the hyperfinite factor, J. Funct. Anal. 240 (2006), 373–398.Google Scholar
6.Jolissaint, P. and Stalder, Y., Strongly singular masas and mixing actions in finite von Neumann algebras, Ergodic Theory Dyn. Syst. 28 (2008), 1861–1878.Google Scholar
7.Kesten, H., Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336–354.CrossRefGoogle Scholar
8.Mukherjee, K., Masas and bimodule decompositions of II1-factors, Q. J. Math. 62 (2011), 451–486.CrossRefGoogle Scholar
9.Mukherjee, K., Singular masas and measure-multiplicity invariant, Houston J. Math. (to appear 2013; arxiv:1104.3507).Google Scholar
10.Neshveyev, S. and Størmer, E., Ergodic theory and maximal abelian subalgebras of the hyperfinite factor, J. Funct. Anal. 195 (2002), 239–261.Google Scholar
11.Popa, S., Orthogonal pairs of *-subalgebras in finite von Neumann algebras, J. Operator Theory 9 (1983), 253–268.Google Scholar
12.Popa, S., Maximal injective subalgebras in factors associated with free groups, Adv. Math. 50 (1983), 27–48.Google Scholar
13.Pukánszky, L., On maximal abelian subrings of factors of type II 1, Canad. J. Math. 12 (1960), 289–296.CrossRefGoogle Scholar
14.Pytlik, T., Radial functions on free groups and a decomposition of the regular representation into irreducible components, J. Reine Angew. Math. 326 (1981), 124–135.Google Scholar
15.Rădulescu, F., Singularity of the radial subalgebra of (FN) and the Pukánszky invariant, Pacific J. Math. 151 (1991), 297–306.Google Scholar
16.Sinclair, A. M. and Smith, R. R., The Laplacian masa in a free group factor, Trans. Amer. Math. Soc. 355 (2003), 465–475 (electronic).CrossRefGoogle Scholar
17.Sinclair, A. M. and Smith, R. R., The Pukánszky invariant for masas in group von Neumann factors, Illinois J. Math. 49 (2005), 325–343 (electronic).CrossRefGoogle Scholar
18.Sinclair, A. M. and Smith, R. R., Finite von Neumann algebras and masas, London Mathematical Society Lecture Note Series, vol. 351 (Cambridge University Press, Cambridge, UK, 2008).Google Scholar
19.Voiculescu, D., The analogues of entropy and Fisher's information measure in free probability theory III: The absence of Cartan subalgebras, Geom. Funct. Anal. 6 (1996), 172–199.Google Scholar