Cyclic Homology and de Rham Homology of Affine Algebras
Author | : Ioannis Emmanouil |
Publisher | : |
Total Pages | : 84 |
Release | : 1994 |
Genre | : |
ISBN | : |
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Author | : Ioannis Emmanouil |
Publisher | : |
Total Pages | : 84 |
Release | : 1994 |
Genre | : |
ISBN | : |
Author | : Jean-Louis Loday |
Publisher | : Springer Science & Business Media |
Total Pages | : 467 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662217392 |
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.
Author | : A. Connes |
Publisher | : American Mathematical Society |
Total Pages | : 592 |
Release | : 2023-02-23 |
Genre | : Mathematics |
ISBN | : 1470469774 |
This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27–October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory. The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme. The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.
Author | : Peter Seibt |
Publisher | : World Scientific |
Total Pages | : 176 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : 9789971504700 |
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.
Author | : Joachim Cuntz |
Publisher | : Springer Science & Business Media |
Total Pages | : 160 |
Release | : 2003-11-17 |
Genre | : Mathematics |
ISBN | : 9783540404699 |
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.
Author | : Dale Husemöller |
Publisher | : |
Total Pages | : 134 |
Release | : 1991 |
Genre | : Algebra, Homological |
ISBN | : |
Author | : Ralf Meyer |
Publisher | : European Mathematical Society |
Total Pages | : 376 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9783037190395 |
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.
Author | : Jean-Louis Loday |
Publisher | : Springer Science & Business Media |
Total Pages | : 525 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662113899 |
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.
Author | : Yves André |
Publisher | : Springer Nature |
Total Pages | : 241 |
Release | : 2020-07-16 |
Genre | : Mathematics |
ISBN | : 303039719X |
"...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables." --Mathematical Reviews
Author | : Joachim J. R. Cuntz |
Publisher | : American Mathematical Soc. |
Total Pages | : 199 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 0821808230 |
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 in June 1995.