TY - JOUR
T1 - ALMOST REPRESENTATIONS OF ALGEBRAS AND QUANTIZATION
AU - Ioos, Louis
AU - Kazhdan, David
AU - Polterovich, Leonid
N1 - Publisher Copyright:
© 2023 by Johns Hopkins University Press.
PY - 2023/10
Y1 - 2023/10
N2 - We introduce the notion of almost representations of Lie algebras and quantum tori, and establish an Ulam-stability type phenomenon: every irreducible almost representation is close to a genuine irreducible representation. As an application, we prove that geometric quantizations of the two-dimensional sphere and the two-dimensional torus are conjugate in the semi-classical limit up to a small error.
AB - We introduce the notion of almost representations of Lie algebras and quantum tori, and establish an Ulam-stability type phenomenon: every irreducible almost representation is close to a genuine irreducible representation. As an application, we prove that geometric quantizations of the two-dimensional sphere and the two-dimensional torus are conjugate in the semi-classical limit up to a small error.
UR - http://www.scopus.com/inward/record.url?scp=85173723055&partnerID=8YFLogxK
U2 - 10.1353/ajm.2023.a907706
DO - 10.1353/ajm.2023.a907706
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AN - SCOPUS:85173723055
SN - 0002-9327
VL - 145
SP - 1587
EP - 1629
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 5
ER -