Comparison and continuity of Wick-type star products on certain coadjoint orbits-Reference-Cited by-同舟云学术

Comparison and continuity of Wick-type star products on certain coadjoint orbits

Published:2019-09-01 Issue:5 Volume:31 Page:1203-1223
ISSN:1435-5337
Container-title:Forum Mathematicum
language:
Short-container-title:

Author:

Esposito Chiara¹,Schmitt Philipp²,Waldmann Stefan³

Affiliation:

1. Dipartimento di Matematica, Università degli Studi di Salerno, via Giovanni Paolo II, 123, 84084Fisciano(SA), Italy

2. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100Copenhagen, Denmark

3. Institut für Mathematik, Lehrstuhl für Mathematik X, Universität Würzburg, Campus Hubland Nord, Emil-Fischer-Str. 31, 97074Würzburg, Germany

Abstract

AbstractIn this paper, we discuss continuity properties of the Wick-type star product on the 2-sphere, interpreted as a coadjoint orbit. Star products on coadjoint orbits in general have been constructed by different techniques. We compare the constructions of Alekseev–Lachowska and Karabegov, and we prove that they agree in general. In the case of the 2-sphere, we establish the continuity of the star product, thereby allowing for a completion to a Fréchet algebra.

Funder

Danmarks Grundforskningsfond

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2018-0302/pdf

Reference80 articles.

1. Quantum differential surfaces of higher genera;Preprint,2017

2. Homogeneous Kähler manifolds: Paving the way towards new supersymmetric sigma models;Comm. Math. Phys.,1986

3. Questions on quantization;Operator Algebras and Operator Theory,1998

4. A simple geometrical construction of deformation quantization;J. Differential Geom.,1994

5. Berezin’s quantization on flag manifolds and spherical modules;Trans. Amer. Math. Soc.,1998

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Convergent star products on cotangent bundles of Lie groups;Mathematische Annalen;2022-04-07

2. Strict quantization of coadjoint orbits;Journal of Noncommutative Geometry;2021-12-15

3. Wick rotations in deformation quantization;Reviews in Mathematical Physics;2021-07-26