Symplectic Poisson And Noncommutative Geometry PDF Download
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Author | : Tohru Eguchi |
Publisher | : Cambridge University Press |
Total Pages | : 303 |
Release | : 2014-08-25 |
Genre | : Mathematics |
ISBN | : 1107056411 |
Download Symplectic, Poisson, and Noncommutative Geometry Book in PDF, ePub and Kindle
This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute.
Author | : Ana Cannas da Silva |
Publisher | : American Mathematical Soc. |
Total Pages | : 202 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9780821809525 |
Download Geometric Models for Noncommutative Algebras Book in PDF, ePub and Kindle
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.
Author | : Xiang Tang |
Publisher | : |
Total Pages | : 294 |
Release | : 2004 |
Genre | : |
ISBN | : |
Download Quantization of Noncommutative Poisson Manifolds Book in PDF, ePub and Kindle
Author | : Daniel Sternheimer |
Publisher | : Springer |
Total Pages | : 392 |
Release | : 1997-07-31 |
Genre | : Mathematics |
ISBN | : |
Download Deformation Theory and Symplectic Geometry Book in PDF, ePub and Kindle
Proceedings of the Ascona Meeting, June 1996
Author | : Giuseppe Dito |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821844237 |
Download Poisson Geometry in Mathematics and Physics Book in PDF, ePub and Kindle
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.
Author | : L. Corwin |
Publisher | : Birkhäuser |
Total Pages | : 0 |
Release | : 2012-10-03 |
Genre | : Mathematics |
ISBN | : 9781461267171 |
Download The Gelfand Mathematical Seminars, 1990–1992 Book in PDF, ePub and Kindle
This Seminar began in Moscow in November 1943 and has continued without interruption up to the present. We are happy that with this vol ume, Birkhiiuser has begun to publish papers of talks from the Seminar. It was, unfortunately, difficult to organize their publication before 1990. Since 1990, most of the talks have taken place at Rutgers University in New Brunswick, New Jersey. Parallel seminars were also held in Moscow, and during July, 1992, at IRES in Bures-sur-Yvette, France. Speakers were invited to submit papers in their own style, and to elaborate on what they discussed in the Seminar. We hope that readers will find the diversity of styles appealing, and recognize that to some extent this reflects the diversity of styles in a mathematical society. The principal aim was to have interesting talks, even if the topic was not especially popular at the time. The papers listed in the Table of Contents reflect some of the rich variety of ideas presented in the Seminar. Not all the speakers submit ted papers. Among the interesting talks that influenced the seminar in an important way, let us mention, for example, that of R. Langlands on per colation theory and those of J. Conway and J. McKay on sporadic groups. In addition, there were many extemporaneous talks as well as short discus sions.
Author | : Alain Connes |
Publisher | : Springer |
Total Pages | : 364 |
Release | : 2003-12-15 |
Genre | : Mathematics |
ISBN | : 3540397027 |
Download Noncommutative Geometry Book in PDF, ePub and Kindle
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Author | : Gwyn Bellamy |
Publisher | : Cambridge University Press |
Total Pages | : 367 |
Release | : 2016-06-20 |
Genre | : Mathematics |
ISBN | : 1107129540 |
Download Noncommutative Algebraic Geometry Book in PDF, ePub and Kindle
This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.
Author | : Simone Gutt |
Publisher | : Cambridge University Press |
Total Pages | : 380 |
Release | : 2005-06-21 |
Genre | : Mathematics |
ISBN | : 9780521615051 |
Download Poisson Geometry, Deformation Quantisation and Group Representations Book in PDF, ePub and Kindle
An accessible introduction to Poisson geometry suitable for graduate students.
Author | : Alain Connes |
Publisher | : American Mathematical Soc. |
Total Pages | : 785 |
Release | : 2019-03-13 |
Genre | : |
ISBN | : 1470450453 |
Download Noncommutative Geometry, Quantum Fields and Motives Book in PDF, ePub and Kindle
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.