代数的概表示和量子化

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2023-10-01 DOI:10.1353/ajm.2023.a907706

Louis Ioos, David Kazhdan, Leonid Polterovich

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引用次数: 2

摘要

引入李代数和量子环面的概表示概念，建立了一个ulam稳定性型现象:每一个不可约概表示都接近于一个真不可约表示。作为一个应用，我们证明了二维球面和二维环面的几何量子化在半经典极限下是共轭的，误差很小。

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Almost representations of algebras and quantization

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.

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.