Non Commutative Gelfand Theories
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Author |
: Steffen Roch |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 388 |
Release |
: 2010-11-19 |
ISBN-10 |
: 9780857291837 |
ISBN-13 |
: 0857291831 |
Rating |
: 4/5 (37 Downloads) |
Synopsis Non-commutative Gelfand Theories by : Steffen Roch
Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a so-called polynomial identity or in short: Pl-algebra). In the second half of the book, a number of selected examples are used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis. Distinguished by the consequent use of local principles (non-commutative Gelfand theories), PI-algebras, Mellin techniques and limit operator techniques, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right. Written in a way that can be worked through by the reader with fundamental knowledge of analysis, functional analysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.
Author |
: Ivan E. Guzman |
Publisher |
: |
Total Pages |
: 64 |
Release |
: 2013 |
ISBN-10 |
: OCLC:871701676 |
ISBN-13 |
: |
Rating |
: 4/5 (76 Downloads) |
Synopsis On a Generalization of the Gelfand Transform to Non-commutative Banach Algebras by : Ivan E. Guzman
A Gelfand theory for an arbitrary Banach algebra A is a pair (G, A), such that: A is a C*-algebra and G : A -> A is an algebra homomorphism; G induces a bijection between the set of maximal modular left ideals of A and the set of maximal modular left ideals of A; and for every maximal modular left ideal L of A, the map G[subscript L] : A/G[superscript -1](L) -> A/L induced by G has dense range. We prove that if A is a postliminal C*-algebra with Gelfand theory (G, A), then no proper C*-subalgebra of A contains GA. We also show that if J is an ideal of a Banach algebra A such that A/J and J both have Gelfand theories, then A also has a Gelfand theory if we impose some conditions on J and on its Gelfand theory.
Author |
: Alain Connes |
Publisher |
: Springer |
Total Pages |
: 364 |
Release |
: 2003-12-15 |
ISBN-10 |
: 9783540397021 |
ISBN-13 |
: 3540397027 |
Rating |
: 4/5 (21 Downloads) |
Synopsis Noncommutative Geometry by : Alain Connes
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.
Author |
: J.L. Bueso |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 307 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9789401702850 |
ISBN-13 |
: 9401702853 |
Rating |
: 4/5 (50 Downloads) |
Synopsis Algorithmic Methods in Non-Commutative Algebra by : J.L. Bueso
The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.
Author |
: Masoud Khalkhali |
Publisher |
: European Mathematical Society |
Total Pages |
: 244 |
Release |
: 2009 |
ISBN-10 |
: 3037190612 |
ISBN-13 |
: 9783037190616 |
Rating |
: 4/5 (12 Downloads) |
Synopsis Basic Noncommutative Geometry by : Masoud Khalkhali
"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 |
: Dmitry S. Kaliuzhnyi-Verbovetskyi |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 194 |
Release |
: 2014-11-19 |
ISBN-10 |
: 9781470416973 |
ISBN-13 |
: 1470416972 |
Rating |
: 4/5 (73 Downloads) |
Synopsis Foundations of Free Noncommutative Function Theory by : Dmitry S. Kaliuzhnyi-Verbovetskyi
In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.
Author |
: Masoud Khalkhali |
Publisher |
: World Scientific |
Total Pages |
: 515 |
Release |
: 2008 |
ISBN-10 |
: 9789812814333 |
ISBN-13 |
: 9812814337 |
Rating |
: 4/5 (33 Downloads) |
Synopsis An Invitation to Noncommutative Geometry by : Masoud Khalkhali
A walk in the noncommutative garden / A. Connes and M. Marcolli -- Renormalization of noncommutative quantum field theory / H. Grosse and R. Wulkenhaar -- Lectures on noncommutative geometry / M. Khalkhali -- Noncommutative bundles and instantons in Tehran / G. Landi and W. D. van Suijlekom -- Lecture notes on noncommutative algebraic geometry and noncommutative tori / S. Mahanta -- Lectures on derived and triangulated categories / B. Noohi -- Examples of noncommutative manifolds: complex tori and spherical manifolds / J. Plazas -- D-branes in noncommutative field theory / R. J. Szabo.
Author |
: Gerald J. Murphy |
Publisher |
: Academic Press |
Total Pages |
: 297 |
Release |
: 2014-06-28 |
ISBN-10 |
: 9780080924960 |
ISBN-13 |
: 0080924964 |
Rating |
: 4/5 (60 Downloads) |
Synopsis C*-Algebras and Operator Theory by : Gerald J. Murphy
This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.
Author |
: Huishi Li |
Publisher |
: CRC Press |
Total Pages |
: 230 |
Release |
: 2021-11-08 |
ISBN-10 |
: 9781000471106 |
ISBN-13 |
: 1000471101 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Noncommutative Polynomial Algebras of Solvable Type and Their Modules by : Huishi Li
Noncommutative Polynomial Algebras of Solvable Type and Their Modules is the first book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. In doing so, this book covers: A constructive introduction to solvable polynomial algebras and Gröbner basis theory for left ideals of solvable polynomial algebras and submodules of free modules The new filtered-graded techniques combined with the determination of the existence of graded monomial orderings The elimination theory and methods (for left ideals and submodules of free modules) combining the Gröbner basis techniques with the use of Gelfand-Kirillov dimension, and the construction of different kinds of elimination orderings The computational construction of finite free resolutions (including computation of syzygies, construction of different kinds of finite minimal free resolutions based on computation of different kinds of minimal generating sets), etc. This book is perfectly suited to researchers and postgraduates researching noncommutative computational algebra and would also be an ideal resource for teaching an advanced lecture course.
Author |
: Peter G. Dodds |
Publisher |
: Springer Nature |
Total Pages |
: 583 |
Release |
: 2024-01-19 |
ISBN-10 |
: 9783031496547 |
ISBN-13 |
: 303149654X |
Rating |
: 4/5 (47 Downloads) |
Synopsis Noncommutative Integration and Operator Theory by : Peter G. Dodds
The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.