**Colloquium Publications**

Volume: 51;
2004;
375 pp;
Hardcover

MSC: Primary 17;
Secondary 14

Print ISBN: 978-0-8218-3528-9

Product Code: COLL/51

List Price: $80.00

AMS Member Price: $64.00

MAA Member Price: $72.00

**Electronic ISBN: 978-1-4704-3197-6
Product Code: COLL/51.E**

List Price: $80.00

AMS Member Price: $64.00

MAA Member Price: $72.00

#### Supplemental Materials

# Chiral Algebras

Share this page
*Alexander Beilinson; Vladimir Drinfeld*

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a one-of-a-kind book featuring previously unpublished material.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.

#### Readership

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

#### Reviews & Endorsements

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

-- Francisco J. Plaza Martin for Mathematical Reviews