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Product Code:  MEMO/254/1213 
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eBook ISBN:  9781470447427 
Product Code:  MEMO/254/1213.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 
Softcover ISBN:  9781470428587 
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Product Code:  MEMO/254/1213.B 
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AMS Member Price:  $93.60 $70.20 
Softcover ISBN:  9781470428587 
Product Code:  MEMO/254/1213 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 
eBook ISBN:  9781470447427 
Product Code:  MEMO/254/1213.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 
Softcover ISBN:  9781470428587 
eBook ISBN:  9781470447427 
Product Code:  MEMO/254/1213.B 
List Price:  $156.00 $117.00 
MAA Member Price:  $140.40 $105.30 
AMS Member Price:  $93.60 $70.20 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 254; 2018; 85 ppMSC: Primary 17; 46; 81
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 onetoone correspondence between the unitary subalgebras \(W\) of \(V\) and the covariant subnets of \(\mathcal A_V\).

Table of Contents

Chapters

1. Introduction

2. Preliminaries on von Neumann algebras

3. Preliminaries on conformal nets

4. Preliminaries on vertex algebras

5. Unitary vertex operator algebras

6. Energy bounds and strongly local vertex operator algebras

7. Covariant subnets and unitary subalgebras

8. Criteria for strong locality and examples

9. Back to vertex operators

A. Vertex algebra locality and Wightman locality

B. On the BisognanoWichmann property for representations of the Mobius̈ group


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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 onetoone correspondence between the unitary subalgebras \(W\) of \(V\) and the covariant subnets of \(\mathcal A_V\).

Chapters

1. Introduction

2. Preliminaries on von Neumann algebras

3. Preliminaries on conformal nets

4. Preliminaries on vertex algebras

5. Unitary vertex operator algebras

6. Energy bounds and strongly local vertex operator algebras

7. Covariant subnets and unitary subalgebras

8. Criteria for strong locality and examples

9. Back to vertex operators

A. Vertex algebra locality and Wightman locality

B. On the BisognanoWichmann property for representations of the Mobius̈ group