Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 4

Special Issue in honor of Victor Guillemin

Guest Editors: Yael Karshon, Richard Melrose, Gunther Uhlmann, and Alejandro Uribe

Symplectic reduction and a Darboux–Moser–Weinstein theorem for Lie algebroids

Pages: 2067 – 2131

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n4.a13

Authors

Yi Lin (Georgia Southern University, Statesboro, Ga., U.S.A.)

Yiannis Loizides (George Mason University, Fairfax, Virginia, U.S.A.)

Reyer Sjamaar (Department of Mathematics, Cornell University, Ithaca, New York, U.S.A.)

Yanli Song (Washington University, St. Louis, Missouri, U.S.A.)

Abstract

We extend the Marsden–Weinstein reduction theorem and the Darboux–Moser–Weinstein theorem to symplectic Lie algebroids. We also obtain a coisotropic embedding theorem for symplectic Lie algebroids.

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Received 8 February 2022

Received revised 31 October 2022

Accepted 29 December 2022

Published 20 November 2023