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Noncommutative Distributions
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Book Synopsis Noncommutative Distributions by : Sergio Albeverio
Download or read book Noncommutative Distributions written by Sergio Albeverio and published by CRC Press. This book was released on 1993-08-26 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary stochastic analysis, Noncommutative Distributions: examines a theory of noncommutative distributions as irreducible unitary representations of groups of mappings from a manifold into a Lie group, with applications to gauge-field theories; describes the energy representation when the target Lie group G is compact; discusses representations of G-valued jet bundles when G is not necessarily compact; and supplies a synthesis of deep results on quasi-simple Lie algebras.;Providing over 200 bibliographic citations, drawings, tables, and equations, Noncommutative Distributions is intended for research mathematicians and theoretical and mathematical physicists studying current algebras, the representation theory of Lie groups, and quantum field theory, and graduate students in these disciplines.
Book Synopsis Noncommutative Harmonic Analysis by : Patrick Delorme
Download or read book Noncommutative Harmonic Analysis written by Patrick Delorme and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to Jacques Carmona, an expert in noncommutative harmonic analysis, the volume presents excellent invited/refereed articles by top notch mathematicians. Topics cover general Lie theory, reductive Lie groups, harmonic analysis and the Langlands program, automorphic forms, and Kontsevich quantization. Good text for researchers and grad students in representation theory.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Noncommutative Stationary Processes by : Rolf Gohm
Download or read book Noncommutative Stationary Processes written by Rolf Gohm and published by Springer Science & Business Media. This book was released on 2004 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Associative and Non-Commutative Algebra and Operator Theory by : Cheikh Thiécoumbe Gueye
Download or read book Non-Associative and Non-Commutative Algebra and Operator Theory written by Cheikh Thiécoumbe Gueye and published by Springer. This book was released on 2016-11-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he has served as a mentor to a generation of mathematicians in Senegal and around the world.
Book Synopsis Topics in Non-Commutative Geometry by : Y. Manin
Download or read book Topics in Non-Commutative Geometry written by Y. Manin and published by Princeton University Press. This book was released on 2014-07-14 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-commutative Analysis by : Palle Jorgensen
Download or read book Non-commutative Analysis written by Palle Jorgensen and published by World Scientific. This book was released on 2017-01-24 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'This is a book to be read and worked with. For a beginning graduate student, this can be a valuable experience which at some points in fact leads up to recent research. For such a reader there is also historical information included and many comments aiming at an overview. It is inspiring and original how old material is combined and mixed with new material. There is always something unexpected included in each chapter, which one is thankful to see explained in this context and not only in research papers which are more difficult to access.'Mathematical Reviews ClippingsThe book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.
Book Synopsis Noncommutative Geometry, Quantum Fields and Motives by : Alain Connes
Download or read book Noncommutative Geometry, Quantum Fields and Motives written by Alain Connes and published by American Mathematical Soc.. This book was released on 2019-03-13 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Engineering Applications of Noncommutative Harmonic Analysis by : Gregory S. Chirikjian
Download or read book Engineering Applications of Noncommutative Harmonic Analysis written by Gregory S. Chirikjian and published by CRC Press. This book was released on 2021-02-25 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.
Book Synopsis Pseudo-Differential Equations And Stochastics Over Non-Archimedean Fields by : Anatoly Kochubei
Download or read book Pseudo-Differential Equations And Stochastics Over Non-Archimedean Fields written by Anatoly Kochubei and published by CRC Press. This book was released on 2001-08-03 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equat
Book Synopsis The Semicircle Law, Free Random Variables and Entropy by : Fumio Hiai
Download or read book The Semicircle Law, Free Random Variables and Entropy written by Fumio Hiai and published by American Mathematical Soc.. This book was released on 2000 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book treats free probability theory, which has been extensively developed since the early 1980s. The emphasis is put on entropy and the random matrix model approach. The volume is a unique presentation demonstrating the extensive interrelation between the topics. Wigner's theorem and its broad generalizations, such as asymptotic freeness of independent matrices, are explained in detail. Consistent throughout the book is the parallelism between the normal and semicircle laws. Voiculescu's multivariate free entropy theory is presented with full proofs and extends the results to unitary operators. Some applications to operator algebras are also given. Based on lectures given by the authors in Hungary, Japan, and Italy, the book is a good reference for mathematicians interested in free probability theory and can serve as a text for an advanced graduate course. This book brings together both new material and recent surveys on some topics in differential equations that are either directly relevant to, or closely associated with, mathematical physics. Its topics include asymptotic formulas for the ground-state energy of fermionic gas, renormalization ideas in quantum field theory from perturbations of the free Hamiltonian on the circle, $J$-selfadjoint Dirac operators, spectral theory of Schrodinger operators, inverse problems, isoperimetric inequalities in quantum mechanics, Hardy inequalities, and non-adiabatic transitions. Excellent survey articles on Dirichlet-Neumann inverse problems on manifolds (by Uhlmann), numerical investigations associated with Laplacian eigenvalues on planar regions (by Trefethen), Snell's law and propagation of singularities in the wave equation (by Vasy), random operators on tree graphs (by Aizenmann) make this book interesting and valuable for graduate students, young mathematicians, and physicists alike.
Book Synopsis Noncommutative Geometry and Physics 3 by : Giuseppe Dito
Download or read book Noncommutative Geometry and Physics 3 written by Giuseppe Dito and published by World Scientific. This book was released on 2013 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.
Book Synopsis Smart Grid using Big Data Analytics by : Robert C. Qiu
Download or read book Smart Grid using Big Data Analytics written by Robert C. Qiu and published by John Wiley & Sons. This book was released on 2017-04-17 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at students in communications and signal processing who want to extend their skills in the energy area. It describes power systems and why these backgrounds are so useful to smart grid, wireless communications being very different to traditional wireline communications.
Book Synopsis Non-commutative Cryptography and Complexity of Group-theoretic Problems by : Alexei G. Myasnikov
Download or read book Non-commutative Cryptography and Complexity of Group-theoretic Problems written by Alexei G. Myasnikov and published by American Mathematical Soc.. This book was released on 2011 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.
Book Synopsis Free Random Variables by : Dan V. Voiculescu
Download or read book Free Random Variables written by Dan V. Voiculescu and published by American Mathematical Soc.. This book was released on 1992 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.
Book Synopsis An Introduction to Noncommutative Geometry by : Joseph C. Várilly
Download or read book An Introduction to Noncommutative Geometry written by Joseph C. Várilly and published by European Mathematical Society. This book was released on 2006 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the conditions on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.
