Division algebras and noncommensurable isospectral manifolds

Alexander Lubotzky, Beth Samuels, Uzi Vishne

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

A. W. Reid [R, Theorem 2.1] showed that if τ1 and τ2 are arithmetic lattices in G = PGL2(R) or in PGL2(ℂ) which give rise to isospectral manifolds, then τ1 and F: are commensurable (after conjugation). We show that for d ≥ 3 and script capital L sign = PGLd(ℝ)/PO d(ℝ) or for script capital L sign = PGLd(ℂ)/ PUd(ℂ), the situation is quite different; there are arbitrarily large finite families of isospectral noncommensurable compact manifolds covered by y. The constructions are based on the arithmetic groups obtained from division algebras with the same ramification points but different invariants.

Original languageEnglish
Pages (from-to)361-380
Number of pages20
JournalDuke Mathematical Journal
Volume135
Issue number2
DOIs
StatePublished - 1 Nov 2006

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