Vertex algebras for beginners. 2nd ed. (English) Zbl 0924.17023

University Lecture Series. 10. Providence, RI: American Mathematical Society (AMS). vi, 201 p. (1998).
[For a review of the first ed. 1996, see Zbl 0861.17017.]
This book provides an interesting and complete presentation of certain important topics in the theory of vertex algebras. The contents of the book is as follows: Chapter 1. Wightman axioms and vertex algebras, Chapter 2. Calculus of formal distributions, Chapter 3. Local fields, Chapter 4. Structure theory of vertex algebras, Chapter 5. Examples of vertex algebras and their applications.
The second edition is an enlarged and improved version of the first edition. Of particular importance are the improvements in Chapter 2, where many new results from the theory of conformal algebras are presented. Chapter 5 brings a new section on super boson-fermion correspondence with applications to number theory, and a complete list of finite simple conformal superalgebras. Some of these new results were conjectured in the first edition of the book. The bibliography is completed with the list of many new papers from the theory of vertex algebras.


17B69 Vertex operators; vertex operator algebras and related structures
17-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics


Zbl 0861.17017