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1 November 2006 Division algebras and noncommensurable isospectral manifolds
Alexander Lubotzky, Beth Samuels, Uzi Vishne
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Duke Math. J. 135(2): 361-379 (1 November 2006). DOI: 10.1215/S0012-7094-06-13525-1

Abstract

A. W. Reid [R, Theorem 2.1] showed that if Γ1 and Γ2 are arithmetic lattices in G=PGL2(R) or in PGL2(C) which give rise to isospectral manifolds, then Γ1 and Γ2 are commensurable (after conjugation). We show that for d3 and S=PGLd(R)/POd(R) or for S=PGLd(C)/PUd(C), the situation is quite different; there are arbitrarily large finite families of isospectral noncommensurable compact manifolds covered by S. The constructions are based on the arithmetic groups obtained from division algebras with the same ramification points but different invariants

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Alexander Lubotzky. Beth Samuels. Uzi Vishne. "Division algebras and noncommensurable isospectral manifolds." Duke Math. J. 135 (2) 361 - 379, 1 November 2006. https://doi.org/10.1215/S0012-7094-06-13525-1

Information

Published: 1 November 2006
First available in Project Euclid: 17 October 2006

zbMATH: 1123.58020
MathSciNet: MR2267287
Digital Object Identifier: 10.1215/S0012-7094-06-13525-1

Subjects:
Primary: 58J35
Secondary: 11F70

Rights: Copyright © 2006 Duke University Press

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Vol.135 • No. 2 • 1 November 2006
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