Differential Forms On Regular Affine Algebra

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Differential Forms On Regular Affine Algebra

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Author : Gerhard Paul Hochschild
language : en
Publisher:
Release Date : 1961

Differential Forms On Regular Affine Algebra written by Gerhard Paul Hochschild and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Differential forms categories.

A mathematical discussion of the algebras of differential forms is treated as a special combination of linear algebra and homological alegbra. There is specific identification of this particular exterior algebra as applied to canical graded algebra based on the Tor functor and obtained by the cohomology of differential forms from the ext functor to a universal algebra i. e. Lie algebra. Attention is directed chiefly to a regular affine algebra, K-algebra, which is Noetherian with a finite Krull dimension, i. e. the largest non-negative integer.

Differential Forms On Regular Affine Algebra

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Author : Gerhard Paul Hochschild
language : en
Publisher:
Release Date : 1961

Differential Forms On Regular Affine Algebra written by Gerhard Paul Hochschild and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Differential forms categories.

Differential Forms In Algebraic Topology

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Author : Raoul Bott
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Differential Forms In Algebraic Topology written by Raoul Bott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

Traces Of Differential Forms And Hochschild Homology

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Author : Reinhold Hübl
language : en
Publisher: Springer
Release Date : 2006-12-08

Traces Of Differential Forms And Hochschild Homology written by Reinhold Hübl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

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.

Residues And Traces Of Differential Forms Via Hochschild Homology

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Author : Joseph Lipman
language : en
Publisher: American Mathematical Soc.
Release Date : 1987

Residues And Traces Of Differential Forms Via Hochschild Homology written by Joseph Lipman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Requiring only some understanding of homological algebra and commutative ring theory, this book gives those who have encountered Grothendieck residues in geometry or complex analysis an understanding of residues, as well as an appreciation of Hochschild homology.

Hochschild Cohomology For Algebras

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Author : Sarah J. Witherspoon
language : en
Publisher: American Mathematical Society
Release Date : 2020-06-30

Hochschild Cohomology For Algebras written by Sarah J. Witherspoon and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-30 with Mathematics categories.

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.

Lectures On Duflo Isomorphisms In Lie Algebra And Complex Geometry

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Author : Damien Calaque
language : en
Publisher: European Mathematical Society
Release Date : 2011

Lectures On Duflo Isomorphisms In Lie Algebra And Complex Geometry written by Damien Calaque and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

The Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflo-type result for $Q$-manifolds. All notions mentioned above are introduced and explained in this book. The only prerequisites are basic linear algebra and differential geometry. In addition to standard notions such as Lie (super) algebras, complex manifolds, Hochschild and Chevalley-Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in detail. This book is well suited for graduate students in mathematics and mathematical physics as well as researchers working in Lie theory, algebraic geometry, and deformation theory.

Poisson Geometry Deformation Quantisation And Group Representations

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Author : Simone Gutt
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-21

Poisson Geometry Deformation Quantisation And Group Representations written by Simone Gutt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Mathematics categories.

An accessible introduction to Poisson geometry suitable for graduate students.

An Invitation To Noncommutative Geometry

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Author : Masoud Khalkhali
language : en
Publisher: World Scientific
Release Date : 2008

An Invitation To Noncommutative Geometry written by Masoud Khalkhali and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.

Formality Theory

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Author : Chiara Esposito
language : en
Publisher: Springer
Release Date : 2014-09-04

Formality Theory written by Chiara Esposito and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-04 with Science categories.

This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.