Noncommutative Localization In Algebra And Topology

Author : Andrew Ranicki
Publisher : Cambridge University Press
Page : 332 pages
File Size : 47,5 Mb
Release : 2006-02-09
Category : Mathematics
ISBN : 052168160X

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Noncommutative Localization in Algebra and Topology by Andrew Ranicki Pdf

Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.

Author : Department of Mathematics and Statistics Andrew Ranicki
Publisher : Unknown
Page : 329 pages
File Size : 52,6 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362822

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Non-Commutative Localization in Algebra and Topology by Department of Mathematics and Statistics Andrew Ranicki Pdf

An introduction to noncommutative localization and an account of the state of the art suitable for researchers and graduate students.

Author : F.M.J. van Oystaeyen,A.H.M.J. Verschoren
Publisher : Springer
Page : 408 pages
File Size : 43,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540386018

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Non-commutative Algebraic Geometry by F.M.J. van Oystaeyen,A.H.M.J. Verschoren Pdf

Author : Jara Pascual,Conchi Vidal,A Verschoren
Publisher : CRC Press
Page : 260 pages
File Size : 42,6 Mb
Release : 1995-11-30
Category : Mathematics
ISBN : 0582273722

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Localization and Sheaves by Jara Pascual,Conchi Vidal,A Verschoren Pdf

This book completely solves the problem of representing rings (and modules over them), which are locally noetherian over subsets of their prime spectrum by structure sheaves over this subset. In order to realise this, one has to develop the necessary localization theory as well as to study local equivalents of familiar concepts like the Artin-Rees property, Ore sets and the second layer condition. The first part of the book is introductory and self-contained, and might serve as a starting course (at graduate level) on localization theory within Grothendieck categories. The second part is more specialised and provides the basic machinery needed to effectively these structure sheaves, as well as to study their functorial behaviour. In this way, the book should be viewed as a first introduction to what should be called relative noncommutative algebraic geometry.

Author : Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss
Publisher : Cambridge University Press
Page : 367 pages
File Size : 49,9 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9781107129542

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Noncommutative Algebraic Geometry by Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss Pdf

This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.

Author : Freddy Van Oystaeyen
Publisher : CRC Press
Page : 310 pages
File Size : 40,5 Mb
Release : 2000-06-06
Category : Mathematics
ISBN : 082470424X

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Algebraic Geometry for Associative Algebras by Freddy Van Oystaeyen Pdf

This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theory that sustains the duality between algebraic geometry and commutative algebra to the noncommutative level.

Author : Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Publisher : Springer
Page : 308 pages
File Size : 52,5 Mb
Release : 2010-10-28
Category : Mathematics
ISBN : 9783642157080

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Topics in Algebraic and Topological K-Theory by Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën Pdf

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

Author : Igor V. Nikolaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 400 pages
File Size : 45,9 Mb
Release : 2022-07-18
Category : Mathematics
ISBN : 9783110788709

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Noncommutative Geometry by Igor V. Nikolaev Pdf

Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.

Author : Jonathan S. Golan
Publisher : CRC Press
Page : 352 pages
File Size : 49,7 Mb
Release : 1975-01-01
Category : Mathematics
ISBN : 0824761987

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Localization of Noncommutative Rings by Jonathan S. Golan Pdf

Author : Christian Ausoni,Kathryn Hess,Jérôme Scherer
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 44,6 Mb
Release : 2009
Category : Algebraic topology
ISBN : 9780821848395

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Alpine Perspectives on Algebraic Topology by Christian Ausoni,Kathryn Hess,Jérôme Scherer Pdf

Contains the proceedings of the Third Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, on August 18-24, 2008. This title includes research papers on stable homotopy theory, the theory of operads, localization and algebraic K-theory, as well as survey papers on the Witten genus and localization techniques.

Author : M. Hazewinkel
Publisher : Elsevier
Page : 592 pages
File Size : 42,9 Mb
Release : 2009-07-08
Category : Mathematics
ISBN : 0080932819

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Handbook of Algebra by M. Hazewinkel Pdf

Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes

Author : C. S. Aravinda,F. T. Farrell,J.-F. Lafont
Publisher : Cambridge University Press
Page : 378 pages
File Size : 50,8 Mb
Release : 2016-01-21
Category : Mathematics
ISBN : 9781107529007

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Geometry, Topology, and Dynamics in Negative Curvature by C. S. Aravinda,F. T. Farrell,J.-F. Lafont Pdf

Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.

Author : A. Rosenberg
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 49,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401584302

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Noncommutative Algebraic Geometry and Representations of Quantized Algebras by A. Rosenberg Pdf

This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others.

Author : Frank Neumann,Sibylle Schroll
Publisher : Springer Nature
Page : 240 pages
File Size : 53,7 Mb
Release : 2020-09-26
Category : Mathematics
ISBN : 9783030517953

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Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants by Frank Neumann,Sibylle Schroll Pdf

This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmüller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.

Author : Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 48,7 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 3540203575

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Noncommutative Geometry by Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts Pdf

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.