3 edition of Topics in algebraic and noncommutative geometry found in the catalog.
Topics in algebraic and noncommutative geometry
Includes bibliographical references
|Statement||Caroline Grant Melles ... [et al.], editors|
|Series||Contemporary mathematics -- 324, Contemporary mathematics (American Mathematical Society) -- v. 324|
|Contributions||Michler, Ruth I. 1967-, Melles, Caroline Grant, 1958-, Annapolis Algebraic Geometry Conference (2001)|
|LC Classifications||QA564 .T655 2003|
|The Physical Object|
|Pagination||xvi, 233 p. :|
|Number of Pages||233|
|LC Control Number||2003043689|
Noncommutative geometry can be expected to say something about topics of arithmetic interest because it provides the right framework for which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic . $\begingroup$ A good method might just be to search for "Artin-Wedderburn theorem" in google books and just pick anything promising from the tons of hits that come back. That is a standard introductory topic in noncommutative algebra. $\endgroup$ – rschwieb Apr 3 '19 at
Textbook Quantum Groups and Noncommutative Geometry. Manin, Y. I. "An introduction to the ideas of algebraic geometry in the motivated context of system theory." This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in. The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. Intended for the graduate students and faculty with interests in noncommutative geometry; they can be read by non-experts. ( views) Very Basic Noncommutative Geometry by Masoud Khalkhali - University of Western Ontario,
This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on. NEW ADDITION: a big list of freely available online courses on algebraic geometry, from introduction to advanced topics, has been compiled in this other a digression on motivation for studying the subject along with a self-learning guide of books is in this new answer.. There are other similar questions, above all asking for references for self-studying, whose answers may be helpful.
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In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on "noncommutative spaces."Cited by: Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes' noncommutative de Rham complex, supergeometry, and.
This book presents the proceedings of two conferences, Résolution des singularités et géométrie non commutative and the Annapolis Algebraic Geometry Conference.
Research articles in the volume cover various topics of algebraic geometry, including the theory of Jacobians, singularities, applications to cryptography, and more. In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on "noncommutative spaces.".
Noncommutative geometry and algebra My main interest is the non-commutative world in all its aspects: geometric, algebraic, topological, physical, et cetera.
Topics in algebraic geometry-Algebraic stacks by A. Kresch A straight way to stacks by M. Romagny (Pre A book by Bodo Pareigis. The aim of this book is to provide a comprehensive introduction to some of the most significant topics in this area, including noncommutative projective algebraic geometry, deformation theory, symplectic reflection algebras, and noncommutative resolutions of singularities.
and basic idea of algebraic geometry. The purpose of this book is to extend this correspondence to the noncommutative case in the framework of real analysis. The theory, called noncommutative geometry, rests on two essential points: 1. The existence of many natural spaces for which the classical set-theoretic tools.
Carlo Rovelli, in Philosophy of Physics, Noncommutative geometry. A geometrical space M admits two alternative descriptions. One is as a set of points x, the other is in terms of a commutative algebra A of functions on M.
In particular, a celebrated result by Gelfand shows that a (compact Hausdorff) space M is determined by the abstract algebra A isomorphic to the algebra of the.
Book Description: There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on.
Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes’ noncommutative de Rham complex, supergeometry, and quantum groups.
They cover a broad spectrum of topics and applications, shedding light on the fruitful interactions between noncommutative geometry and a multitude of areas of contemporary research, such as operator algebras, K-theory, cyclic homology, index theory, spectral theory, geometry of groupoids and in particular of foliations.
In the context of noncommutative geometry, according to Serre-Swan theorem, a non commutative vector bundle is defined as a finitely generated projective module over a noncommutative C* algebra. The topics covered range from Morse theory and complex geometry theory to geometric group theory, and are accompanied by exercises that are designed to deepen the reader's understanding and to guide them in exciting directions for future investigation.
There are many interactions between noncommutative algebra and representation theory on the one hand and classical algebraic geometry on the other, with important applications in both directions.
The aim of this book is to provide a comprehensive introduction to some of the most significant topics in this area, including noncommutative projective algebraic geometry, deformation theory Cited by: This book provides a comprehensive introduction to some of the most significant interactions between noncommutative algebra and representation theory and classical algebraic geometry, including noncommutative projective algebraic geometry, deformation theory, symplectic reflection algebras, and noncommutative resolutions of by: Carlo Rovelli, in Philosophy of Physics, Noncommutative geometry.
A geometrical space M admits two alternative descriptions. One is as a set of points x, the other is in terms of a commutative algebra A of functions on M. In particular, a celebrated result by Gelfand shows that a (compact Hausdorff) space M is determined by the abstract algebra A isomorphic to the algebra of.
ISBN: OCLC Number: Notes: "M.B. Porter lectures"--Page [ii]. Description: pages ; 25 cm: Contents: An overview --Supersymmetric algebraic curves --Flag superspaces and Schubert supercells --Quantum groups as symmetries of quantum Titles.
Topics of particular interest include noncommutative projective algebraic geometry, noncommutative resolutions of (commutative or noncommutative) singularities,Calabi-Yau algebras, deformation theory and Poisson structures, as well as the interplay of these subjects with the algebras appearing in representation theory--like enveloping algebras.
Beginning with division rings arising from geometry, the study of noncommutative rings has grown into a major area of modern algebra. The theory and exposition of noncommutative rings was expanded and refined in the 19th and 20th centuries by numerous authors. This is a monograph on the noncommutative generalisation of Riemannian geometry.
It covers topics such as Hopf algebras, cyclic cohomology, as well as noncommutative analogues of complex structures and Riemannian geometry.
There are applications to physics in the form of quantum spacetime. The study of algebraic groups is part of algebraic geometry, having deep connections to Lie groups and Lie algebras (J.
Grabowski, P. Levy, M. MacDonald). Noncommutative Geometry Noncommutative geometry looks at noncommutative rings and algebras as if they were rings of functions on certain `noncommutative spaces'.
Topics in Non-Commutative Geometry by Y. Manin, Paperback | Barnes & Noble® There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the Our Stores Are OpenBook AnnexMembershipEducatorsGift CardsStores & EventsHelpPages: Buy Noncommutative Geometry by Connes, Alain (ISBN: ) from Amazon's Book Store.
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