Download or read book Cyclic Homology Of Algebras written by Peter Seibt and published by World Scientific. This book was released on 1987-12-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is purely algebraic and concentrates on cyclic homology rather than on cohomology. It attempts to single out the basic algebraic facts and techniques of the theory.The book is organized in two chapters. The first chapter deals with the intimate relation of cyclic theory to ordinary Hochschild theory. The second chapter deals with cyclic homology as a typical characteristic zero theory.
Download or read book Cyclic Homology written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.
Download or read book Cyclic Homology written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter In this second edition the authors have added a chapter 13 on MacLane (co)homology.
Download or read book Cyclic Homology in Non Commutative Geometry written by Joachim Cuntz and published by Springer Science & Business Media. This book was released on 2003-11-17 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.
Download or read book Lectures on Cyclic Homology written by Dale Husemöller and published by . This book was released on 1991 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cyclic Homology in Non Commutative Geometry written by Joachim Cuntz and published by Springer. This book was released on 2011-01-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.
Download or read book Local and Analytic Cyclic Homology written by Ralf Meyer and published by European Mathematical Society. This book was released on 2007 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book, the author develops and compares these theories, emphasizing their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to $K$-theory, and the Chern-Connes character for $K$-theory and $K$-homology. The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras. Some chapters are more elementary and independent of the rest of the book and will be of interest to researchers and students working on functional analysis and its applications.
Download or read book Bivariant Periodic Cyclic Homology written by Christian Groenbaek and published by CRC Press. This book was released on 1999-04-30 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent work by Cuntz and Quillen on bivariant periodic cyclic homology has caused quite a revolution in the subject. In this self-contained exposition, the author's purpose is to understand the functorial properties of the Cuntz-Quillen theory, which motivaties his explorations of what he calls cyclic pro-homology. Simply stated, the cyclic pro-homology of an (associative) algebra A is short for the Z/2 Z-graded inverse system of cyclic homology groups of A, considered as a pro-vector space. The author finds that this functor, taking algebras over a field k of characteristic zero into the category of pro-k-vector spaces, is remarkable. He presents a proof that it is excisive and that it satisfies a Künneth isomorphism for the tensor product of algebras. He explains the relation to the Cuntz-Quillen groups in a Universal Coefficient Theorem and in a Milnor lim1-sequence. This enables the lifting - to some extent- of the nice properties of cyclic pro-homology properties to the Cuntz Quillen theory itself. It is interesting to note that for the excision result, this lifting procedure goes through without constraints. For those new to cyclic homology, Dr. Grønbaek takes care to provide an introduction to the subject, including the motivation for the theory, definitions, and fundamental results, and establishes the homological machinery needed for application to the Cuntz-Quillen theory. Mathematicians interested in cyclic homology-especially ring theorists using homological methods-will find this work original, enlightening, and thought-provoking. The author leaves the door open for deeper study into excision for the Cuntz-Quillen theory for a class of topological algebras, such as the category of m-algebras considered by Cuntz.
Download or read book String Topology and Cyclic Homology written by Ralph L. Cohen and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores string topology, Hochschild and cyclic homology, assembling material from a wide scattering of scholarly sources in a single practical volume. The first part offers a thorough and elegant exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology.
Download or read book Cyclic Homology of Algebras written by Peter Seibt and published by World Scientific. This book was released on 1987 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is purely algebraic and concentrates on cyclic homology rather than on cohomology. It attempts to single out the basic algebraic facts and techniques of the theory.The book is organized in two chapters. The first chapter deals with the intimate relation of cyclic theory to ordinary Hochschild theory. The second chapter deals with cyclic homology as a typical characteristic zero theory.
Download or read book An Introduction to Homological Algebra written by Charles A. Weibel and published by Cambridge University Press. This book was released on 1995-10-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
Download or read book The Local Structure of Algebraic K Theory written by Bjørn Ian Dundas and published by Springer Science & Business Media. This book was released on 2012-09-06 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
Download or read book Hochschild Cohomology for Algebras written by Sarah J. Witherspoon and published by American Mathematical Society. This book was released on 2020-06-30 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a thorough and self-contained introduction to the theory of Hochschild cohomology for algebras and includes many examples and exercises. The book then explores Hochschild cohomology as a Gerstenhaber algebra in detail, the notions of smoothness and duality, algebraic deformation theory, infinity structures, support varieties, and connections to Hopf algebra cohomology. Useful homological algebra background is provided in an appendix. The book is designed both as an introduction for advanced graduate students and as a resource for mathematicians who use Hochschild cohomology in their work.
Download or read book Cyclic Cohomology and Noncommutative Geometry written by Joachim J. R. Cuntz and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry is a new field that is among the great challenges of present-day mathematics. Its methods allow one to treat noncommutative algebras - such as algebras of pseudodifferential operators, group algebras, or algebras arising from quantum field theory - on the same footing as commutative algebras, that is, as spaces. Applications range over many fields of mathematics and mathematical physics. This volume contains the proceedings of the workshop on "Cyclic Cohomology and Noncommutative Geometry" held at The Fields Institute (Waterloo, ON) in June 1995. The workshop was part of the program for the special year on operator algebras and its applications.
Download or read book Topics in Cyclic Theory written by Daniel G. Quillen and published by Cambridge University Press. This book was released on 2020-07-09 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988–92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on noncommutative differential forms, quasi-free algebras and Chern characters on connections.
Download or read book Operads in Algebra Topology and Physics written by Martin Markl and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.
Download or read book The Homology of Banach and Topological Algebras written by A.Y. Helemskii and published by Springer Science & Business Media. This book was released on 1989-10-31 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi *.... si j'avait su comment en revenir. One service mathematics has rendered the human race. It has put common sense back je n'y serais point aUe.' it belongs. on the topmost shelf next Jules Verne where to the dusty canister labelled 'discarded non· The series is divergent: therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
