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Symplectic Geometry, Groupoids and Integrable Systems
Pierre Dazord,Alan Weinstein +1 more
- 01 May 1991
62
About: The article was published on 01 May 1991. and is currently open access. The article focuses on the topics: Symplectomorphism & Moment map.
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Citations
•Book
Geometric Models for Noncommutative Algebras
Ana Cannas da Silva,Alan Weinstein +1 more
- 01 Jun 1999
TL;DR: The Poincare-Birkhoff-Witt theorem as discussed by the authors describes a Poisson geometry for algebraic deformation theory, which is a generalization of Weyl algebras.
•Posted Content
Rieffel induction as generalized quantum Marsden-Weinstein reduction
TL;DR: In this paper, a new approach to quantization of constrained or otherwise reduced classical mechanical systems is proposed, based on the generalized symplectic reduction procedure of Mikami and Weinstein, as further extended by Xu in connection with symplectic equivalence bimodules and Morita equivalence of Poisson manifolds.
91
Dirac structures, momentum maps, and quasi-Poisson manifolds
Henrique Bursztyn,Marius Crainic +1 more
TL;DR: In this article, the correspondence between Poisson maps and actions of symplectic groupoids was extended to Dirac geometry by constructing an inversion procedure relating quasi-Poisson bivectors to twisted Dirac structures.
Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds
TL;DR: In this article, the authors describe the quantization of 2-plectic manifolds as they arise in the context of the quantum geometry of M-branes and non-geometric flux compactifications of closed string theory.
40
On locally conformal symplectic manifolds of the first kind
TL;DR: In this paper, the authors studied locally conformal symplectic structures of the first kind on compact nilmanifolds which do not admit Vaisman metrics and showed that they are the product of a real line with a compact contact manifold.
35