Hamiltonian Lie Algebroids
| Author | : Christian Blohmann |
| Publisher | : American Mathematical Society |
| Total Pages | : 112 |
| Release | : 2024-04-17 |
| Genre | : Mathematics |
| ISBN | : 147046909X |
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Hamiltonian Lie Algebroids
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General Theory of Lie Groupoids and Lie Algebroids
| Author | : Kirill C. H. Mackenzie |
| Publisher | : Cambridge University Press |
| Total Pages | : 540 |
| Release | : 2005-06-09 |
| Genre | : Mathematics |
| ISBN | : 0521499283 |
This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry andgeneral connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles. As such, this book will be of great interest to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.
Poisson Structures
| Author | : Camille Laurent-Gengoux |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 470 |
| Release | : 2012-08-27 |
| Genre | : Mathematics |
| ISBN | : 3642310907 |
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.
Geometric Models for Noncommutative Algebras
| Author | : Ana Cannas da Silva |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 202 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9780821809525 |
The volume is based on a course, ``Geometric Models for Noncommutative Algebras'' taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids. Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.
Lie Groupoids and Lie Algebroids in Differential Geometry
| Author | : K. Mackenzie |
| Publisher | : Cambridge University Press |
| Total Pages | : 345 |
| Release | : 1987-06-25 |
| Genre | : Mathematics |
| ISBN | : 052134882X |
This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory.
Differential Geometry and Its Applications
| Author | : Old?ich Kowalski |
| Publisher | : World Scientific |
| Total Pages | : 732 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9812790608 |
This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture ?Leonhard Euler ? 300 years on? by R Wilson. Notable contributors include J F Cari¤ena, M Castrill¢n L¢pez, J Erichhorn, J-H Eschenburg, I Kol ?, A P Kopylov, J Korba?, O Kowalski, B Kruglikov, D Krupka, O Krupkov , R Landre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Mu¤oz Masqu, S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slov k, J Szilasi, L Tam ssy, P Walczak, and others.
Differential Geometry And Its Applications - Proceedings Of The 10th International Conference On Dga2007
| Author | : Demeter Krupka |
| Publisher | : World Scientific |
| Total Pages | : 732 |
| Release | : 2008-07-14 |
| Genre | : Mathematics |
| ISBN | : 9814471941 |
This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture “Leonhard Euler — 300 years on” by R Wilson. Notable contributors include J F Cariñena, M Castrillón López, J Erichhorn, J-H Eschenburg, I Kolář, A P Kopylov, J Korbaš, O Kowalski, B Kruglikov, D Krupka, O Krupková, R Léandre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Muñoz Masqué, S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slovák, J Szilasi, L Tamássy, P Walczak, and others.
The Breadth of Symplectic and Poisson Geometry
| Author | : Jerrold E. Marsden |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 666 |
| Release | : 2007-07-03 |
| Genre | : Mathematics |
| ISBN | : 0817644199 |
* The invited papers in this volume are written in honor of Alan Weinstein, one of the world’s foremost geometers * Contributions cover a broad range of topics in symplectic and differential geometry, Lie theory, mechanics, and related fields * Intended for graduate students and working mathematicians, this text is a distillation of prominent research and an indication of future trends in geometry, mechanics, and mathematical physics
Multiple Facets of Quantization and Supersymmetry
| Author | : M. A. Olshanetsky |
| Publisher | : World Scientific |
| Total Pages | : 914 |
| Release | : 2002 |
| Genre | : Science |
| ISBN | : 9789812777065 |
This book is dedicated to the memory of Michael Marinov, the theorist who, together with Felix Berezin, introduced the classical description of spin by anticommuting Grassmann variables. It contains original papers and reviews by physicists and mathematicians written specifically for the book. These articles reflect the current status and recent developments in the areas of Marinov''s research: quantum tunneling, quantization of constrained systems, supersymmetry, and others. The personal recollections included portray the human face of M Marinov, a person of great knowledge and integrity.
Handbook of Pseudo-Riemannian Geometry and Supersymmetry
| Author | : Vicente Cortés |
| Publisher | : European Mathematical Society |
| Total Pages | : 972 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 9783037190791 |
The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with torsion Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on Lorentzian manifolds D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory, and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kahler geometry or generalized geometry.
