Yuri I. Manin's Books

Methods of Homological Algebra

By: Sergei I. Gelfand,Yuri I. Manin

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Methods of Homological Algebra

By: Sergei I. Gelfand,Yuri I. Manin

This modern approach to homological algebra by two leading writers in the field is based on the systematic use of the language and ideas of derived categories and derived functors. It describes relations with standard cohomology theory and provides complete proofs. Coverage also presents basic concepts and results of homotopical algebra. This second edition contains numerous corrections.

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Page Count

390

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662124920

ISBN 13

9783662124925

Gauge Field Theory and Complex Geometry

By: Yuri I. Manin

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Gauge Field Theory and Complex Geometry

By: Yuri I. Manin

From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.

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Page Count

368

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540613781

ISBN 13

9783540613787

Quantum Groups and Noncommutative Geometry

By: Yuri I. Manin

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Quantum Groups and Noncommutative Geometry

By: Yuri I. Manin

This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others. This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin's lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka–Krein formalism, which further strengthens Manin's approach to symmetry and moduli-objects in noncommutative geometry.

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Page Count

122

Publisher

Springer

Published Date

ISBN 10

3319979876

ISBN 13

9783319979878

Introduction to the Theory of Schemes

By: Yuri I. Manin

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Introduction to the Theory of Schemes

By: Yuri I. Manin

This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas. "This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson

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217

Publisher

Springer

Published Date

ISBN 10

3319743163

ISBN 13

9783319743165

Topics in Non-Commutative Geometry

By: Y. Manin

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Topics in Non-Commutative Geometry

By: Y. Manin

There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on "noncommutative spaces." Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes' noncommutative de Rham complex, supergeometry, and quantum groups. He then discusses supersymmetric algebraic curves that arose in connection with superstring theory; examines superhomogeneous spaces, their Schubert cells, and superanalogues of Weyl groups; and provides an introduction to quantum groups. This book is intended for mathematicians and physicists with some background in Lie groups and complex geometry. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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Page Count

173

Publisher

Princeton University Press

Published Date

ISBN 10

1400862515

ISBN 13

9781400862511

Introduction to the Theory of Schemes

By: Yuri I. Manin

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Introduction to the Theory of Schemes

By: Yuri I. Manin

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217

Publisher

Springer

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ISBN 10

3319743163

ISBN 13

9783319743165

Book's by Yuri I. Manin

Methods of Homological Algebra

Methods of Homological Algebra

Gauge Field Theory and Complex Geometry

Gauge Field Theory and Complex Geometry

Quantum Groups and Noncommutative Geometry

Quantum Groups and Noncommutative Geometry

Introduction to the Theory of Schemes

Introduction to the Theory of Schemes

Topics in Non-Commutative Geometry

Topics in Non-Commutative Geometry

Introduction to the Theory of Schemes

Introduction to the Theory of Schemes

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