Hochschild Cohomology For Algebras

Author : Sarah J. Witherspoon
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 49,7 Mb
Release : 2019-12-10
Category : Education
ISBN : 9781470449315

Get Book

Hochschild Cohomology for Algebras by Sarah J. Witherspoon Pdf

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.

Author : Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang
Publisher : Springer Nature
Page : 349 pages
File Size : 47,6 Mb
Release : 2022-01-21
Category : Mathematics
ISBN : 9783030373269

Get Book

Differential Equations on Manifolds and Mathematical Physics by Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang Pdf

This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.

Author : Allan M. Sinclair,Roger R. Smith
Publisher : Cambridge University Press
Page : 208 pages
File Size : 51,5 Mb
Release : 1995-03-09
Category : Mathematics
ISBN : 9780521478809

Get Book

Hochschild Cohomology of Von Neumann Algebras by Allan M. Sinclair,Roger R. Smith Pdf

This is an introductory text intended to give the non-specialist a comprehensive insight into the science of biotransformations. The book traces the history of biotransformations, clearly spells out the pros and cons of conducting enzyme-mediated versus whole-cell bioconversions, and gives a variety of examples wherein the bio-reaction is a key element in a reaction sequence leading from cheap starting materials to valuable end products.

Author : P Seibt
Publisher : World Scientific
Page : 172 pages
File Size : 51,7 Mb
Release : 1987-12-01
Category : Mathematics
ISBN : 9789814551182

Get Book

Cyclic Homology of Algebras by P Seibt Pdf

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. Contents:IntroductionCyclic (Co)homology and Hochschild (Co)homology — Preliminaries: Spectral Sequences, Cyclic (Co)homology and Hochschild (Co)homologyParticularities in Characteristic Zero — Relation to de Rham Theory, Relation to Lie TheoryComments and ReferencesFurther ReferencesList of Symbols and NotationsIndex Readership: Mathematicians and theoretical physicists. Keywords:Cyclic Homology;Cohomology;Hochschild Theory;Characteristic Zero;Lie Theory

Author : Michiel Hazewinkel,Murray Gerstenhaber
Publisher : Springer Science & Business Media
Page : 1024 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400930575

Get Book

Deformation Theory of Algebras and Structures and Applications by Michiel Hazewinkel,Murray Gerstenhaber Pdf

This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).

Author : Allan M. Sinclair,Roger R. Smith
Publisher : Unknown
Page : 206 pages
File Size : 42,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362148

Get Book

Hochschild Cohomology of Von Neumann Algebras by Allan M. Sinclair,Roger R. Smith Pdf

The continuous Hochschild cohomology of dual normal modules over a von Neumann algebra is the subject of this book. The necessary technical results are developed assuming a familiarity with basic C*-algebra and von Neumann algebra theory, including the decomposition into two types, but no prior knowledge of cohomology theory is required and the theory of completely bounded and multilinear operators is given fully. Central to this book are those cases when the continuous Hochschild cohomology H[superscript n](M, M) of the von Neumann algebra M over itself is zero. The material in this book lies in the area common to Banach algebras, operator algebras and homological algebra, and will be of interest to researchers from these fields.

Author : Reinhold Hübl
Publisher : Springer
Page : 115 pages
File Size : 51,9 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540461258

Get Book

Traces of Differential Forms and Hochschild Homology by Reinhold Hübl Pdf

This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms. The approach uses Hochschild-homology, the definition of which is extended to the category of topological algebras. Many results for Hochschild-homology of commutative algebras also hold for Hochschild-homology of topological algebras. In particular, after introducing an appropriate notion of completion of differential algebras, one gets a natural transformation between differential forms and Hochschild-homology of topological algebras. Traces of differential forms are of interest to everyone working with duality theory and residue symbols. Hochschild-homology is a useful tool in many areas of k-theory. The treatment is fairly elementary and requires only little knowledge in commutative algebra and algebraic geometry.

Author : Sarah J. Witherspoon
Publisher : American Mathematical Society
Page : 265 pages
File Size : 53,6 Mb
Release : 2020-06-30
Category : Mathematics
ISBN : 9781470462864

Get Book

Hochschild Cohomology for Algebras by Sarah J. Witherspoon Pdf

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.

Author : E. Christensen,A. M. Sinclair
Publisher : Unknown
Page : 20 pages
File Size : 53,7 Mb
Release : 1988
Category : Electronic
ISBN : OCLC:897704602

Get Book

On the Hochschild Cohomology for Von Neumann Algebras by E. Christensen,A. M. Sinclair Pdf

Author : Simon Lentner,Svea Nora Mierach,Christoph Schweigert,Yorck Sommerhäuser
Publisher : Springer Nature
Page : 76 pages
File Size : 43,5 Mb
Release : 2023-07-25
Category : Science
ISBN : 9789811946455

Get Book

Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I by Simon Lentner,Svea Nora Mierach,Christoph Schweigert,Yorck Sommerhäuser Pdf

The book addresses a key question in topological field theory and logarithmic conformal field theory: In the case where the underlying modular category is not semisimple, topological field theory appears to suggest that mapping class groups do not only act on the spaces of chiral conformal blocks, which arise from the homomorphism functors in the category, but also act on the spaces that arise from the corresponding derived functors. It is natural to ask whether this is indeed the case. The book carefully approaches this question by first providing a detailed introduction to surfaces and their mapping class groups. Thereafter, it explains how representations of these groups are constructed in topological field theory, using an approach via nets and ribbon graphs. These tools are then used to show that the mapping class groups indeed act on the so-called derived block spaces. Toward the end, the book explains the relation to Hochschild cohomology of Hopf algebras and the modular group.

Author : Reiner Hermann:
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 50,9 Mb
Release : 2016-09-06
Category : Associative rings
ISBN : 9781470419950

Get Book

Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology by Reiner Hermann: Pdf

In this monograph, the author extends S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore the author establishes an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, the author shows that his construction behaves well with respect to structure preserving functors between exact monoidal categories. The author uses his main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, he further determines a significant part of the Lie bracket's kernel, and thereby proves a conjecture by L. Menichi. Along the way, the author introduces n-extension closed and entirely extension closed subcategories of abelian categories, and studies some of their properties.

Author : Charles A. Weibel
Publisher : Cambridge University Press
Page : 470 pages
File Size : 51,8 Mb
Release : 1995-10-27
Category : Mathematics
ISBN : 9781139643078

Get Book

An Introduction to Homological Algebra by Charles A. Weibel Pdf

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.

Author : Alexander Zimmermann
Publisher : Springer
Page : 720 pages
File Size : 52,5 Mb
Release : 2014-08-15
Category : Mathematics
ISBN : 9783319079684

Get Book

Representation Theory by Alexander Zimmermann Pdf

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 44,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662217399

Get Book

Cyclic Homology by Jean-Louis Loday Pdf

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 : Jean-Louis Loday
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 52,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662113899

Get Book

Cyclic Homology by Jean-Louis Loday Pdf

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.