Geometric Models For Noncommutative Algebras PDF Download
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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 | : 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 | : Igor V. Nikolaev |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 276 |
Release | : 2017-11-07 |
Genre | : Mathematics |
ISBN | : 311054525X |
Download Noncommutative Geometry Book in PDF, ePub and Kindle
This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field. Contents Part I: Basics Model examples Categories and functors C∗-algebras Part II: Noncommutative invariants Topology Algebraic geometry Number theory Part III: Brief survey of NCG Finite geometries Continuous geometries Connes geometries Index theory Jones polynomials Quantum groups Noncommutative algebraic geometry Trends in noncommutative geometry
Author | : Corrado De Concini |
Publisher | : CRC Press |
Total Pages | : 266 |
Release | : 2005-09-01 |
Genre | : Mathematics |
ISBN | : 1420028103 |
Download Noncommutative Algebra and Geometry Book in PDF, ePub and Kindle
A valuable addition to the Lecture Notes in Pure and Applied Mathematics series, this reference results from a conference held in St. Petersburg, Russia, in honor of Dr. Z. Borevich. This volume is mainly devoted to the contributions related to the European Science Foundation workshop, organized under the framework of noncommuntative geometry and i
Author | : Masoud Khalkhali |
Publisher | : European Mathematical Society |
Total Pages | : 244 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9783037190616 |
Download Basic Noncommutative Geometry Book in PDF, ePub and Kindle
"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.
Author | : F.M.J. van Oystaeyen |
Publisher | : Springer |
Total Pages | : 408 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540386017 |
Download Non-commutative Algebraic Geometry Book in PDF, ePub and Kindle
Author | : Lieven Le Bruyn |
Publisher | : CRC Press |
Total Pages | : 592 |
Release | : 2007-08-24 |
Genre | : Mathematics |
ISBN | : 1420064231 |
Download Noncommutative Geometry and Cayley-smooth Orders Book in PDF, ePub and Kindle
Noncommutative Geometry and Cayley-smooth Orders explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. In particular, the book describes the etale local structure of such orders as well as their central singularities and finite dimensional representations. After an introduction to partial d
Author | : Linsen Chou |
Publisher | : |
Total Pages | : 0 |
Release | : 2015-08 |
Genre | : |
ISBN | : 9781681171883 |
Download Introduction to Noncommutative Algebra Book in PDF, ePub and Kindle
A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which xy does not always equal yx; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions. The main motivation is to extend the commutative duality between spaces and functions to the noncommutative setting. In mathematics, spaces, which are geometric in nature, can be related to numerical functions on them. In general, such functions will form a commutative ring. For instance, one may take the ring C(X) of continuous complex-valued functions on a topological space X. In many cases, we can recover X from C(X), and therefore it makes some sense to say that X has commutative topology. The dream of noncommutative geometry is to generalize this duality to the duality between noncommutative algebras, or sheaves of noncommutative algebras, or sheaf-like noncommutative algebraic or operator-algebraic structures and geometric entities of certain kind, and interact between the algebraic and geometric description of those via this duality. Regarding that the commutative rings correspond to usual affine schemes, and commutative C*-algebras to usual topological spaces, the extension to noncommutative rings and algebras requires non-trivial generalization of topological spaces, as "non-commutative spaces". This book provides an elementary introduction to noncommutative rings and algebras.
Author | : Masoud Khalkhali |
Publisher | : American Mathematical Soc. |
Total Pages | : 176 |
Release | : 2011 |
Genre | : Algebra, Homological |
ISBN | : 0821848496 |
Download Perspectives on Noncommutative Geometry Book in PDF, ePub and Kindle
This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008. Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture. Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples. Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume. This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.
Author | : Jose M. Gracia-Bondia |
Publisher | : Springer Science & Business Media |
Total Pages | : 692 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 1461200059 |
Download Elements of Noncommutative Geometry Book in PDF, ePub and Kindle