On Axiomatic Approaches to Vertex Operator Algebras and Modules (Memoirs of the American Mathematical Society) by Igor B. Frenkel (PDF)

Description

The notion of vertex operator algebra arises naturally in the vertex operator construction of the Monster—the largest sporadic finite simple group. From another perspective, the theory of vertex operator algebras and their modules forms the algebraic foundation of conformal field theory. Vertex operator algebras and conformal field theory are now known to be deeply related to many important areas of mathematics. This essentially self-contained monograph develops the basic axiomatic theory of vertex operator algebras and their modules and intertwining operators, following a fundamental analogy with Lie algebra theory. The main axiom, the “Jacobi(-Cauchy) identity”, is a far-reaching analog of the Jacobi identity for Lie algebras. The authors show that the Jacobi identity is equivalent to suitably formulated rationality, commutativity, and associativity properties of products of quantum fields. A number of other foundational and useful results are also developed. This work was originally distributed as a preprint in 1989, and in view of the current widespread interest in the subject among mathematicians and theoretical physicists, its publication and availability should prove no less useful than when it was written.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐

⭐

Keywords

Free Download On Axiomatic Approaches to Vertex Operator Algebras and Modules (Memoirs of the American Mathematical Society) in PDF format
On Axiomatic Approaches to Vertex Operator Algebras and Modules (Memoirs of the American Mathematical Society) PDF Free Download
Download On Axiomatic Approaches to Vertex Operator Algebras and Modules (Memoirs of the American Mathematical Society) 1993 PDF Free
On Axiomatic Approaches to Vertex Operator Algebras and Modules (Memoirs of the American Mathematical Society) 1993 PDF Free Download
Download On Axiomatic Approaches to Vertex Operator Algebras and Modules (Memoirs of the American Mathematical Society) PDF
Free Download Ebook On Axiomatic Approaches to Vertex Operator Algebras and Modules (Memoirs of the American Mathematical Society)