From Vertex Operator Algebras to Conformal Nets and Back

✍ Scribed by Sebastiano Carpi; Yasuyuki Kawahigashi; Roberto Longo

Publisher: American Mathematical Society
Year: 2018
Tongue: English
Leaves: 97
Series: Memoirs of the American Mathematical Society Ser.
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

The authors consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. They present a general procedure which associates to every strongly local vertex operator algebra $V$ a conformal net $\mathcal A_V$ acting on the Hilbert space completion of $V$ and prove that the isomorphism class of $\mathcal A_V$ does not depend on the choice of the scalar product on $V$. They show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra $V$, the map $W\mapsto \mathcal A_W$ gives a one-to-one correspondence between the unitary subalgebras $W$ of $V$ and the covariant subnets of $\mathcal A_V$.

✦ Subjects

Vertex operator algebras. ; Conformal invariants.; MAT000000; NON000000; NON000000

📜 SIMILAR VOLUMES

Two-Dimensional Conformal Geometry and V

📁 Two-Dimensional Conformal Geometry and Vertex Operator Algebras

✍ Yi-Zhi Huang (auth.) 📂 Library 📅 1995 🏛 Birkhäuser Basel 🌐 English

"The exposition is clear and accessible. The necessary background material...is explained in detail in three appendices [and] another appendix consists of answers to some exercises formulated in the text... Self-contained to a high degree... Highly recommended."--ZAA</STR

Two-Dimensional Conformal Geometry and V

📁 Two-Dimensional Conformal Geometry and Vertex Operator Algebras (Progress in Mathematics)

✍ Yi-Zhi Huang 📂 Library 📅 2011 🏛 Birkhäuser 🌐 English

The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc tures of conformal field theories. Much of the recent progress has deep con

Introduction to Vertex Operator Algebras

📁 Introduction to Vertex Operator Algebras and Their Representations

✍ James Lepowsky, Haisheng Li (auth.) 📂 Library 📅 2004 🏛 Birkhäuser Basel 🌐 English

"…[The] authors give a systematic introduction to the theory of vertex operator algebras and their representations. Particular emphasis is put on the axiomatic development of the theory and the construction theorems for vertex operator algebras and their modules. The book provides a detailed s

Generalized Vertex Algebras and Relative

📁 Generalized Vertex Algebras and Relative Vertex Operators

✍ Chongying Dong, James Lepowsky (auth.) 📂 Library 📅 1993 🏛 Birkhäuser Basel 🌐 English

The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. They are mathematically precise counterparts of what are known in

On Axiomatic Approaches to Vertex Operat

📁 On Axiomatic Approaches to Vertex Operator Algebras and Modules

✍ Igor B. Frenkel, Yi-Zhi Huang, James Lepowsky 📂 Library 📅 1993 🏛 Amer Mathematical Society 🌐 English

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 op

On Axiomatic Approaches to Vertex Operat

📁 On Axiomatic Approaches to Vertex Operator Algebras and Modules

✍ Igor B. Frenkel, Yi-Zhi Huang, James Lepowsky 📂 Library 📅 1993 🏛 Amer Mathematical Society 🌐 English