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Chiral Algebras

Alexander Beilinson University of Chicago, Chicago, IL
Vladimir Drinfeld University of Chicago, Chicago, IL
Available Formats:
Hardcover ISBN: 978-0-8218-3528-9
Product Code: COLL/51
List Price: $85.00 MAA Member Price:$76.50
AMS Member Price: $68.00 Electronic ISBN: 978-1-4704-3197-6 Product Code: COLL/51.E List Price:$80.00
MAA Member Price: $72.00 AMS Member Price:$64.00
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List Price: $127.50 MAA Member Price:$114.75
AMS Member Price: $102.00 Click above image for expanded view Chiral Algebras Alexander Beilinson University of Chicago, Chicago, IL Vladimir Drinfeld University of Chicago, Chicago, IL Available Formats:  Hardcover ISBN: 978-0-8218-3528-9 Product Code: COLL/51  List Price:$85.00 MAA Member Price: $76.50 AMS Member Price:$68.00
 Electronic ISBN: 978-1-4704-3197-6 Product Code: COLL/51.E
 List Price: $80.00 MAA Member Price:$72.00 AMS Member Price: $64.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$127.50 MAA Member Price: $114.75 AMS Member Price:$102.00
• Book Details

Colloquium Publications
Volume: 512004; 375 pp
MSC: Primary 17; Secondary 14;

This long-awaited publication contains the results of the research of two distinguished professors from the University of Chicago, Alexander Beilinson and Fields Medalist, Vladimir Drinfeld. Years in the making, this is a one-of-a-kind book featuring previously unpublished material.

Chiral algebras form the primary algebraic structure of modern conformal field theory. Each chiral algebra lives on an algebraic curve, and in the special case where this curve is the affine line, chiral algebras invariant under translations are the same as well-known and widely used vertex algebras.

The exposition of this book covers the following topics:

• the “classical” counterpart of the theory, which is an algebraic theory of non-linear differential equations and their symmetries;
• the local aspects of the theory of chiral algebras, including the study of some basic examples, such as the chiral algebras of differential operators;
• the formalism of chiral homology treating “the space of conformal blocks” of the conformal field theory, which is a “quantum” counterpart of the space of the global solutions of a differential equation.

The book is intended for researchers working in algebraic geometry and its applications to mathematical physics and representation theory.

Graduate students and research mathematicians interested in algebraic geometry and its applications to field theory.

• Chapters
• Introduction
• Chapter 1. Axiomatic patterns
• Chapter 2. Geometry of $\mathcal {D}$-schemes
• Chapter 3. Local theory: Chiral basics
• Chapter 4. Global theory: Chiral homology

• Reviews

• Without a doubt, it will become a standard reference on the subject.

Francisco J. Plaza Martin for Mathematical Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 512004; 375 pp
MSC: Primary 17; Secondary 14;

This long-awaited publication contains the results of the research of two distinguished professors from the University of Chicago, Alexander Beilinson and Fields Medalist, Vladimir Drinfeld. Years in the making, this is a one-of-a-kind book featuring previously unpublished material.

Chiral algebras form the primary algebraic structure of modern conformal field theory. Each chiral algebra lives on an algebraic curve, and in the special case where this curve is the affine line, chiral algebras invariant under translations are the same as well-known and widely used vertex algebras.

The exposition of this book covers the following topics:

• the “classical” counterpart of the theory, which is an algebraic theory of non-linear differential equations and their symmetries;
• the local aspects of the theory of chiral algebras, including the study of some basic examples, such as the chiral algebras of differential operators;
• the formalism of chiral homology treating “the space of conformal blocks” of the conformal field theory, which is a “quantum” counterpart of the space of the global solutions of a differential equation.

The book is intended for researchers working in algebraic geometry and its applications to mathematical physics and representation theory.

Graduate students and research mathematicians interested in algebraic geometry and its applications to field theory.

• Chapters
• Introduction
• Chapter 1. Axiomatic patterns
• Chapter 2. Geometry of $\mathcal {D}$-schemes
• Chapter 3. Local theory: Chiral basics
• Chapter 4. Global theory: Chiral homology
• Without a doubt, it will become a standard reference on the subject.

Francisco J. Plaza Martin for Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.