Deformation Problems In Lie Algebroids And Extended Poisson Geometry
DOWNLOAD
Download Deformation Problems In Lie Algebroids And Extended Poisson Geometry PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Deformation Problems In Lie Algebroids And Extended Poisson Geometry book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Deformation Problems In Lie Algebroids And Extended Poisson Geometry
DOWNLOAD
Author : Xiang Ji
language : en
Publisher:
Release Date : 2013
Deformation Problems In Lie Algebroids And Extended Poisson Geometry written by Xiang Ji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Poisson Geometry Deformation Quantisation And Group Representations
DOWNLOAD
Author : Simone Gutt
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-21
Poisson Geometry Deformation Quantisation And Group Representations written by Simone Gutt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Mathematics categories.
An accessible introduction to Poisson geometry suitable for graduate students.
Poisson Geometry In Mathematics And Physics
DOWNLOAD
Author : Giuseppe Dito
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Poisson Geometry In Mathematics And Physics written by Giuseppe Dito and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Poisson Structures And Lie Algebroids In Complex Geometry
DOWNLOAD
Author : Brent Pym
language : en
Publisher:
Release Date : 2013
Poisson Structures And Lie Algebroids In Complex Geometry written by Brent Pym and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Nonlinear Poisson Brackets
DOWNLOAD
Author : Mikhail Vladimirovich Karasev
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Nonlinear Poisson Brackets written by Mikhail Vladimirovich Karasev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.
Nonlinear Poisson Brackets
DOWNLOAD
Author : Mihail Vladimirovi_ Karasev
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-06-06
Nonlinear Poisson Brackets written by Mihail Vladimirovi_ Karasev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-06 with Education categories.
This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.
Lie Methods In Deformation Theory
DOWNLOAD
Author : Marco Manetti
language : en
Publisher: Springer Nature
Release Date : 2022-08-01
Lie Methods In Deformation Theory written by Marco Manetti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-01 with Mathematics categories.
This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.
Deformation Theory Of Algebras And Structures And Applications
DOWNLOAD
Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Deformation Theory Of Algebras And Structures And Applications written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).
Poisson Structures
DOWNLOAD
Author : Camille Laurent-Gengoux
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-27
Poisson Structures written by Camille Laurent-Gengoux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-27 with Mathematics categories.
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.
A Geometric Approach To Lie Systems
DOWNLOAD
Author : Eduardo Fernández Saiz
language : en
Publisher:
Release Date : 2021
A Geometric Approach To Lie Systems written by Eduardo Fernández Saiz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
The notion of quantum algebras is merged with that of Lie systems in order to establish a new formalism called Poisson–Hopf algebra deformations of Lie systems. The procedure can be naturally applied to Lie systems endowed with a symplectic structure, the so-called Lie–Hamilton systems.This is quite a general approach, as it can be applied to any quantum deformation and any underlying manifold. One of its main features is that, under quantum deformations, Lie systems are extended to generalized systems described by involutive distributions. As a consequence, a quantum deformed Lie system no longer has an underlying Vessiot–Guldberg Lie algebra or a quantum algebra one, but keeps a Poisson–Hopf algebra structure that enables us to obtain, in an explicit way, the t-independent constants of the motion from quantum deformed Casimir invariants, which are potentially useful in a further construction of the generalized notion of superposition rules. We illustrate this approach by considering the non-standard quantum deformation of sl(2) applied to well-known Lie systems, such as the oscillator problem or Milne–Pinney equation, as well as several types of Riccati equations. In this way, we obtain their new generalized (deformed) counterparts that cover, in particular, a new oscillator system with a time-dependent frequency and a position-dependent mass...