Quantum Groups And Noncommutative Geometry
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Quantum Groups And Noncommutative Geometry
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Author : Yuri I. Manin
language : en
Publisher: Springer
Release Date : 2018-10-11
Quantum Groups And Noncommutative Geometry written by Yuri I. Manin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-11 with Mathematics categories.
This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others. This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin's lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka–Krein formalism, which further strengthens Manin's approach to symmetry and moduli-objects in noncommutative geometry.
Quantum Groups And Noncommutative Spaces
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Author : Matilde Marcolli
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-02
Quantum Groups And Noncommutative Spaces written by Matilde Marcolli 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 2010-11-02 with Mathematics categories.
This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.
Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes
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Author : Gerhard Grensing
language : en
Publisher: World Scientific
Release Date : 2021-07-15
Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes written by Gerhard Grensing and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-15 with Science categories.
The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.
Quantum Groups And Non Commutative Geometry
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Author : Jurij I. Manin
language : en
Publisher: Centre De Recherches Mathematiques
Release Date : 1988
Quantum Groups And Non Commutative Geometry written by Jurij I. Manin and has been published by Centre De Recherches Mathematiques this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Algebra - Asociativne algebre - Nekomutativna geometrija categories.
Topics In Non Commutative Geometry
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Author : Yuri I. Manin
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Topics In Non Commutative Geometry written by Yuri I. Manin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
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. 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." 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. He then discusses supersymmetric algebraic curves that arose in connection with superstring theory; examines superhomogeneous spaces, their Schubert cells, and superanalogues of Weyl groups; and provides an introduction to quantum groups. This book is intended for mathematicians and physicists with some background in Lie groups and complex geometry. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Noncommutative Geometry Quantum Fields And Motives
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Author : Alain Connes
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-03-13
Noncommutative Geometry Quantum Fields And Motives written by Alain Connes 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 2019-03-13 with Mathematics categories.
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.
Quantum Groups And Noncommutative Geometry
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Author : Shahn Majid
language : en
Publisher:
Release Date : 2004
Quantum Groups And Noncommutative Geometry written by Shahn Majid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Geometry, Algebraic categories.
Quantum Groups Noncommutative Geometry And Fundamental Physical Interactions
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Author : Daniel Kastler
language : en
Publisher:
Release Date : 1999
Quantum Groups Noncommutative Geometry And Fundamental Physical Interactions written by Daniel Kastler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Contents include: Hochschild Homology of Function Algebras Associated with Singularities; On the KK-Theory of Stable Projective Limits; Noncommutative Integrability; Gauge Invariance of the Chern-Simons Action in Noncommutative Geometry; The Analysis of the Hochshild Homology; Coproducts and Operations on Cyclic Cohomology; Powers of Quantum Matrices and Relations Between Them; Introductory Notes on Extensions of Hopf Algebras; Hopf Algebras from the Quantum Geometry Point of View; Equation Pentagonale, Bige bres et Espaces de Modules; Chiral Anomalies in the Spectral Action; Standard Model and Unimodularity Condition; On Feynman Graphs as Elements of a Hopf Algebra.
Lectures On Algebraic Quantum Groups
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Author : John C Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-01
Lectures On Algebraic Quantum Groups written by John C Brown 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 2002-04-01 with Mathematics categories.
This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.