ALMOST REPRESENTATIONS OF ALGEBRAS AND QUANTIZATION

Louis Ioos; David Kazhdan; Leonid Polterovich

doi:10.1353/ajm.2023.a907706

ALMOST REPRESENTATIONS OF ALGEBRAS AND QUANTIZATION

Louis Ioos
, David Kazhdan
, Leonid Polterovich

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1587-1629
Number of pages	43
Journal	American Journal of Mathematics
Volume	145
Issue number	5
DOIs	https://doi.org/10.1353/ajm.2023.a907706
State	Published - Oct 2023

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© 2023 by Johns Hopkins University Press.

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10.1353/ajm.2023.a907706

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ALMOST REPRESENTATIONS OF ALGEBRAS AND QUANTIZATION

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