From Vertex Operator Algebras to Conformal Nets and Back (eBook)

Sebastiano Carpi (Autor)

eBook Download: PDF

2018
85 Seiten
American Mathematical Society (Verlag)
978-1-4704-4742-7 (ISBN)

Infos

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 $/mathcal A_V$.

Produkt-Details

• Erscheint lt. Verlag: 8.9.2018
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• ISBN-10: 1-4704-4742-8 / 1470447428
• ISBN-13: 978-1-4704-4742-7 / 9781470447427