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)



Weak amenability of right-angled Coxeter groups

Author: Alain Valette
Journal: Proc. Amer. Math. Soc. 119 (1993), 1331-1334
MSC: Primary 46L99; Secondary 22D99, 43A30
MathSciNet review: 1172955
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the representation-theoretic result of Januszkiewicz has an impact on harmonic analysis and operator algebras; more precisely, right-angled Coxeter groups are weakly amenable with Cowling-Haagerup constant $ 1$; as a consequence, von Neumann algebras with Cowling-Haagerup constant $ > 1$ are not embeddable into the von Neumann algebra of a right-angled Coxeter group.

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

  • [BP] M. Bozejko and M. Picardello, Weakly amenable groups and amalgamated products, Proc. Amer. Math. Soc. 117 (1993), 1039-1046. MR 1119263 (93e:43005)
  • [CJ] A. Connes and V. F. R. Jones, Property (T) for von Neumann algebras, Bull. London Math. Soc. 17 (1985), 57-62. MR 766450 (86a:46083)
  • [CH] M. Cowling and U. Haagerup, Completely bounded multipliers of The Fourier algebra of a simple Lie group of real rank one, Invent. Math. 96 (1989), 507-549. MR 996553 (90h:22008)
  • [Cu] J. Cuntz, $ K$-theoretic amenability for discrete groups, J. Reine Angew. Math. 344 (1983), 180-195. MR 716254 (86e:46064)
  • [De] A. Deutsch, Kazhdan's property (T) and related properties of loally compact and discrete groups, Ph.D. thesis, Univ. of Edinburgh, 1992.
  • [Ja] T. Januszkiewicz, For right-angled Coxeter groups $ {z^{\vert g\vert}}$ is a coefficient of a uniformly bounded representation, Proc. Amer. Math. Soc. 119 (1993), 1115-1119. MR 1172951 (94a:20066)
  • [JV] P. Jolissaint and A. Valette, Normes de Sobolev et convoluteurs bornés sur $ {L^2}(G)$, Ann. Inst. Fourier (Grenoble) 41 (1991), 797-822. MR 1150567 (93d:43004)
  • [Pi] M. Pimsner, $ KK$-groups of crossed products by groups acting on trees, Invent. Math. 86 (1986), 603-634. MR 860685 (88f:22022)
  • [Sz] R. Szwarc, Groups acting on trees and approximation properties of the Fourier algebra, J. Funct. Anal. 95 (1991), 320-343. MR 1092129 (92e:43005)
  • [V1] A. Valette, Cocycles d'arbres et représentations uniformément bornées, C. R. Acad. Sci. Paris Sér. I 310 (1990), 703-708. MR 1055232 (91i:22008)
  • [V2] -, Les représentations uniformément bornées associées à un arbre réel, Bull. Soc. Math. Belg. 42 (1990), 747-760.
  • [V3] -, Weak forms of amenability for split rank $ 1\;p$-adic groups, $ p$-Adic Methods and their Applications (A. J. Baker and R. J. Plymen, eds.), Oxford Science Publ., Clarendon Press, Oxford, 1992, pp. 143-165.
  • [Zy] A. Zygmund, Trigonometrical series, 2nd ed., Chelsea, New York, 1952. MR 0076084 (17:844d)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L99, 22D99, 43A30

Retrieve articles in all journals with MSC: 46L99, 22D99, 43A30

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society