Poisson Structures and Their Normal Forms

This book is a very good introduction to contemporary research in the field of Poisson structures. Its first chapter serves as an introduction to the theory for beginners. The subsequent chapters then introduce the reader to deeper parts of the theory. Four chapters are devoted to the subject mentioned explicitly in the title, namely the normal forms of Poisson structures, including the Poisson cohomology, the Levi decomposition of Poisson structures, the linearization of Poisson structures, and multiplicative and quadratic Poisson structures (including Poisson-Lie groups and their relations to r-matrices). Then we find a very interesting chapter about Nambu structures. The last two chapters are devoted to Lie groupoids and Lie algebroids. There is also an appendix where various notions are explained, which should help the reader to understand the main text of the book.

The book also contains quite recent results, even some results which are so far not published. The presentation is really very good and even the beginner will find not just a good introduction into the subject but also further reading, which will bring him smoothly to areas of present research. There are many examples that help in the understanding of the theory. The reader can test his or her knowledge by solving the many exercises contained in the book. The book fills a gap in the literature and is indispensable for specialists in the field. In short, it is very well written and can be strongly recommended.

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EUR 48

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