On the Haagerup inequality and groups acting on \(\tilde A_ n\)-buildings

DOI10.5802/aif.1596zbMath0886.51003OpenAlexW2010434682MaRDI QIDQ1369887

Alain Valette

Publication date: 20 October 1997

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1997__47_4_1195_0

zbMATH Keywords

random walksamenabilitygrowth of groupseuclidean buildingsconvolutor norm

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Sums of independent random variables; random walks (60G50) Measures on groups and semigroups, etc. (43A05) Buildings and the geometry of diagrams (51E24)

Related Items (7)

On the loop inequality for euclidean buildings ⋮ Radial rapid decay does not imply rapid decay ⋮ Introduction to the Rapid Decay property ⋮ Strong Haagerup inequalities for free \(\mathfrak R\)-diagonal elements ⋮ Property (RD) for Hecke pairs ⋮ Radial rapid decay property for cocompact lattices ⋮ The rapid decay property and centroids in groups

Cites Work

• K-theory of reduced \(C^*\)-algebras and rapidly decreasing functions on groups
• Groups acting simply transitively on the vertices of a building of type \(\tilde A_ 2\). II: The cases \(q=2\) and \(q=3\)
• Normes de Sobolev et convoluteurs bornés sur \(L^ 2(G)\). (Sobolev norms and bounded convolvers on \(L^ 2(G)\))
• An example of a non nuclear C*-algebra, which has the metric approximation property
• A Haagerup inequality for \(\widetilde A_1\times\widetilde A_1\) and \(\widetilde A_2\) buildings
• A family of \(\widetilde A_n\)-groups
• Property \((T)\) and \(\widetilde{A}_ 2\) groups
• On the loop inequality for euclidean buildings
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• On spectra of simple random walks on one-relator groups. With an appendix by Paul Jolissaint
• Orbihedra of nonpositive curvature
• Free subgroups in linear groups
• Symmetric Random Walks on Groups
• Rapidly Decreasing Functions in Reduced C ∗ -Algebras of Groups
• Computing Norms in Group C ∗ -Algebras
• Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature
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