From Vertex Operator Algebras To Conformal Nets And Back
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From Vertex Operator Algebras to Conformal Nets and Back
Author: Sebastiano Carpi
language: en
Publisher: American Mathematical Soc.
Release Date: 2018-08-09
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 AV acting on the Hilbert space completion of V and prove that the isomorphism class of AV 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↦AW gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of AV.
Vertex Operator Algebras, Number Theory and Related Topics
Author: Matthew Krauel
language: en
Publisher: American Mathematical Soc.
Release Date: 2020-07-13
This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11–15, 2018, at California State University, Sacramento, California. The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present. The proceedings center around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.
Tensor Categories for Vertex Operator Superalgebra Extensions
Author: Thomas Creutzig
language: en
Publisher: American Mathematical Society
Release Date: 2024-04-17
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