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Algebraic aspects of compatible poisson structures ab 63.9 € als Taschenbuch: A study on algebraic properties of compatible Poisson brackets that preserved under bi-Hamiltonian system. Aus dem Bereich: Bücher, Wissenschaft, Mathematik,

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The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.

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Algebraic aspects of compatible poisson structures ab 63.9 EURO A study on algebraic properties of compatible Poisson brackets that preserved under bi-Hamiltonian system

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The book consists of three chapters. In chapter I, we introduce some notions and definitions for basic concepts of the theory of integrable bi-Hamiltonian systems. Several open problems related to our main results are also mentioned in this part. In chapter II. We applied the so-called Jordan-Kronecker decomposition theorem to study algebraic properties of the pencil generated by two constant compatible Poisson structures on a vector space. In particular, we study the linear automorphism group that preserves the pencil. In classical symplectic geometry, many fundamental results are based on the symplectic group, which preserves the symplectic structure. Therefore in the theory of bi-Hamiltonian structures, we hope the linear automorphism group also plays a fundamental role. In chapter III, We describe the Lie group of linear automorphisms of the pencil, and obtain an explicit formula for the dimension of the Lie group and discuss some other algebraic properties such as solvability and Levi-Malcev decomposition.

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Planetary theory discusses the variation of the orbital elements of the solar system planets, through the theory of perturbation. Many theories were introduced to study this variation. The most powerful Hamiltonian mechanics procedures are adopted and explained clearly in this book. This book is recommended and directed to graduate students and researchers in dynamical astronomy and applied mathematics. The style is comprehensive and authoritative. We deal, with the construction of semi analytic Hamiltonian J - S planetary theory in terms of Poincaré canonical variables. The methods of work could be extended to be implemented, for the case of n planets (point masses), yielding more precise algebraic and numerical results, using the Jacobi - Radau system of origins, assuming any order in planetary masses. The terms of the Poisson series are truncated at power 6 at most in the eccentricity - inclination. The book includes the Macsyma programs used to obtain the expansion of the disturbing function up to order 6, in eccentricity - inclination, which is the upper limit of power for a personal computer. The expansion of -n took the space of 3400 pages in the site of internet.

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Operad theory is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity. Operads generalize the various associativity properties already observed in algebras and coalgebras such as Lie algebras or Poisson algebras by modeling computational trees within the algebra. Algebras are to operads as group representations are to groups. Originating from work in algebraic topology by Boardman and Vogt, and J. Peter May (to whom their name is due), it has more recently found many applications, drawing for example on work by Maxim Kontsevich on graph homology.

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The theory of Lie algebras and algebraic groups has been an area of active research for the last 50 years. It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the final chapters. All the prerequisites on commutative algebra and algebraic geometry are included.

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This volume contains the Proceedings of the conference "Complex and Differential Geometry 2009", held at Leibniz Universität Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists from differential geometry and (complex) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in (classical) algebraic geometry through complex geometry, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology.

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