TY - JOUR
T1 - Division algebras and noncommensurable isospectral manifolds
AU - Lubotzky, Alexander
AU - Samuels, Beth
AU - Vishne, Uzi
PY - 2006/11/1
Y1 - 2006/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33751525088&partnerID=8YFLogxK
U2 - 10.1215/S0012-7094-06-13525-1
DO - 10.1215/S0012-7094-06-13525-1
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:33751525088
SN - 0012-7094
VL - 135
SP - 361
EP - 380
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 2
ER -