[Une Note sur l'algèbre de von Neumann d'un groupe de Baumslag–Solitar]
Nous étudions des propriétés qualitatives de l'algèbre de von Neumann d'un groupe de Baumslag–Solitar. À savoir, nous démontrons que, dans le cas non-moyennable et C.C.I., le facteur associé est premier, n'est pas solide, et n'a pas de sous-algèbre de Cartan.
We study qualitative properties of the von Neumann algebra of a Baumslag–Solitar group. Namely, we prove that, in the non-amenable and ICC case, the associated factor is prime, not solid, and does not have any Cartan subalgebra.
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@article{CRMATH_2011__349_1-2_25_0,
author = {Fima, Pierre},
title = {A {Note} on the von {Neumann} algebra of a {Baumslag{\textendash}Solitar} group},
journal = {Comptes Rendus. Math\'ematique},
pages = {25--27},
publisher = {Elsevier},
volume = {349},
number = {1-2},
year = {2011},
doi = {10.1016/j.crma.2010.12.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.12.008/}
}
TY - JOUR AU - Fima, Pierre TI - A Note on the von Neumann algebra of a Baumslag–Solitar group JO - Comptes Rendus. Mathématique PY - 2011 SP - 25 EP - 27 VL - 349 IS - 1-2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.12.008/ DO - 10.1016/j.crma.2010.12.008 LA - en ID - CRMATH_2011__349_1-2_25_0 ER -
%0 Journal Article %A Fima, Pierre %T A Note on the von Neumann algebra of a Baumslag–Solitar group %J Comptes Rendus. Mathématique %D 2011 %P 25-27 %V 349 %N 1-2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.12.008/ %R 10.1016/j.crma.2010.12.008 %G en %F CRMATH_2011__349_1-2_25_0
Fima, Pierre. A Note on the von Neumann algebra of a Baumslag–Solitar group. Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 25-27. doi : 10.1016/j.crma.2010.12.008. http://www.numdam.org/articles/10.1016/j.crma.2010.12.008/
[1] Bass–Serre rigidity results in von Neumann algebras, Duke Math. J., Volume 153 (2010), pp. 23-54
[2] P. Fima, S. Vaes, HNN extensions and unique group measure space decomposition of factors, Trans. Amer. Math. Soc., , in press. | arXiv
[3] New a-T-menable HNN-extension, J. Lie Theory, Volume 13 (2003) no. 2, pp. 383-385
[4] Applications of free entropy to finite von Neumann algebras, II, Ann. of Math., Volume 147 (1998), pp. 143-157
[5] Strongly solid group factors which are not interpolated free group factors, Math. Ann., Volume 346 (2010), pp. 969-989
[6] C. Houdayer, D. Shlyakhtenko, Strongly solid factors with an exotic MASA, Int. Math. Res. Not. IMRN, , in press. | arXiv
[7] On the isomorphisms of Baumslag–Solitar groups, Ukrain. Mat. Zh., Volume 43 (1991) no. 12, pp. 1684-1686 (in Russian)
[8] Solid von Neumann algebras, Acta Math., Volume 192 (2004), pp. 111-117
[9] On a class of factors with at most one Cartan subalgebra, Ann. of Math. (2), Volume 172 (2010) no. 1, pp. 713-749
[10] On a class of factors with at most one Cartan subalgebra, II, Amer. J. Math., Volume 132 (2010) no. 3, pp. 841-866
[11] Strong rigidity of II1 factors arising from malleable actions of w-rigid groups, I, Invent. Math., Volume 165 (2006), pp. 369-408
[12] On the superrigidity of malleable actions with spectral gap, J. Amer. Math. Soc., Volume 21 (2008), pp. 981-1000
[13] Moyennabilité intérieure et extensions HNN, Ann. Inst. Fourier, Volume 56 (2006) no. 2, pp. 309-323
[14] The analogues of entropy and of Fisher's information measure in free probability theory, III, GAFA, Geom. Funct. Anal., Volume 6 (1996), pp. 172-199
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