From Vertex Operator Algebras to Conformal Nets and Back
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-2858-7 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2858-7 (ISBN)
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Considers unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. The authors 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 $V$.
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 $/mathcal A_V$.
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 $/mathcal A_V$.
Introduction;
Preliminaries on von Neumann algebras;
Preliminaries on conformal nets;
Preliminaries on vertex algebras;
Unitary vertex operator algebras;
Energy bounds and strongly local vertex operator algebras;
Covariant subnets and unitary subalgebras;
Criteria for strong locality and examples;
Back to vertex operators;
Appendix A. Vertex algebra locality and Wightman locality;
Appendix B. On the Bisognano-Wichmann property for representations of the Mobius group;
Bibliography.
| Erscheinungsdatum | 21.09.2018 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 189 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-4704-2858-X / 147042858X |
| ISBN-13 | 978-1-4704-2858-7 / 9781470428587 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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