Normal Forms In Poisson Geometry
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Normal Forms in Poisson Geometry
Author | : Ioăn Tiberiu Marcut̨ |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 2013 |
Genre | : Normal forms (Mathematics) |
ISBN | : 903935913X |
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Normal Forms in Poisson Geometry
Author | : Ioăn Tiberiu Marcut̨ |
Publsiher | : Unknown |
Total Pages | : 267 |
Release | : 2013 |
Genre | : Normal forms (Mathematics) |
ISBN | : 903935913X |
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Poisson Structures and Their Normal Forms
Author | : Jean-Paul Dufour,Nguyen Tien Zung |
Publsiher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2006-01-17 |
Genre | : Mathematics |
ISBN | : 9783764373351 |
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The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.
Poisson Geometry in Mathematics and Physics
Author | : Giuseppe Dito,Jiang-Hua Lu,Yoshiaki Maeda |
Publsiher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 2008 |
Genre | : Geometric quantization |
ISBN | : 9780821844236 |
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This volume is a collection of articles by speakers at the Poisson 2006 conference. The program for Poisson 2006 was an overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction.
Quantum Algebras and Poisson Geometry in Mathematical Physics
Author | : Mikhail Vladimirovich Karasev,Elena M. Novikova,Yurii Mikhailovich Vorobjev |
Publsiher | : American Mathematical Soc. |
Total Pages | : 296 |
Release | : 2005 |
Genre | : Computers |
ISBN | : 0821840401 |
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Presents applications of Poisson geometry to some fundamental well-known problems in mathematical physics. This volume is suitable for graduate students and researchers interested in mathematical physics. It uses methods such as: unexpected algebras with non-Lie commutation relations, dynamical systems theory, and semiclassical asymptotics.
Lectures on Poisson Geometry
Author | : Marius Crainic,Rui Loja Fernandes,Ioan Mărcuţ |
Publsiher | : American Mathematical Soc. |
Total Pages | : 479 |
Release | : 2021-09-14 |
Genre | : Education |
ISBN | : 9781470464301 |
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This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way. —Alan Weinstein, University of California at Berkeley This well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study. —Eckhard Meinrenken, University of Toronto
Coherent Transform Quantization and Poisson Geometry
Author | : Mikhail Vladimirovich Karasev |
Publsiher | : American Mathematical Soc. |
Total Pages | : 376 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 0821811789 |
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This volume copntains three extensive articles written by Karasev and his pupils. Topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate symplectic leaves in Poisson manifolds. The articles contain many examples (including from physics) and complete proofs.
Poisson Structures
Author | : Camille Laurent-Gengoux,Anne Pichereau,Pol Vanhaecke |
Publsiher | : Springer Science & Business Media |
Total Pages | : 470 |
Release | : 2012-08-27 |
Genre | : Mathematics |
ISBN | : 9783642310904 |
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Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.