Vertex algebras and geometry

✍ Scribed by Creutzig, Thomas; Linshaw, Andrew R.

• Publisher: American Mathematical Society
• Year: 2018
• Tongue: English
• Leaves: 178
• Series: Contemporary mathematics (American Mathematical Society) 711.
• Category: Library

✦ Synopsis

This book contains the proceedings of the AMS Special Session on Vertex Algebras and Geometry, held from October 8-9, 2016, and the mini-conference on Vertex Algebras, held from October 10-11, 2016, in Denver, Colorado. The papers cover vertex algebras in connection with geometry and tensor categories, with topics in vertex rings, chiral algebroids, the Higgs branch conjecture, and applicability and use of vertex tensor categories.  Read more...

✦ Table of Contents

Cover
Title page
Contents
Introduction
Strongly homotopy chiral algebroids
1. Introduction
2. TDO
3. Picard-Lie ∞-algebroids
4. Beilinson-Drinfeld
5. CDO
6. Chiral ∞-algebroids
References
Associated varieties and Higgs branches (a survey)
1. Associated varieties of vertex algebras
2. Lisse and quasi-lisse vertex algebras
3. Irreducibility conjecture and examples of quasi-lisse vertex algebras
4. BL²PR² correspondence and Higgs branch conjecture
Acknowledgments
References
Vertex rings and their Pierce bundles
1. Introduction
2. Basic properties of vertex rings 3. Derivations4. Characterizations of vertex rings
5. Categories of vertex rings
6. The center of a vertex ring
7. Virasoro vertex -algebras
8. Étale bundles of vertex rings
9. Pierce bundles of vertex rings
10. Von Neumann regular vertex rings
11. Equivalence of some categories of vertex rings
12. Appendices
References
Cosets of the ^{ }( ₄, { })-algebra
1. Introduction
2. Vertex algebras
3. The algebra \cW^{ }( ₄, { })
4. The (1)-orbifold of \cW^{ }( ₄, { })^{ (1)} 5. The Heisenberg coset of \cW^{ }( ₄, { })6. Simple current extensions and \cW_{ℓ}( { }, { })
References
A sufficient condition for convergence and extension property for strongly graded vertex algebras
1. Introduction
2. Strongly graded vertex algebras and their modules
3. ₁-cofiniteness condition
4. Logarithmic intertwining operators
5. Differential equations
6. The regularity of the singular points
7. Braided tensor category structure
References
On infinite order simple current extensions of vertex operator algebras
1. Introduction
2. Background 3. Sum completion of a category \CCC4. Constructing lattice VOAs
Acknowledgments
References
Back Cover

✦ Subjects

Vertex operator algebras -- Congresses;Operator algebras -- Congresses;Geometry, Algebraic -- Congresses;Quantum theory -- Groups and algebras in quantum theory -- Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations;Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Vertex operators;vertex operator algebras and related structures;Geometry, Algebraic;Operator algebra