Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

**Conformal nets and KK-theory.** / Carpi, Sebastiano; Conti, Roberto ; Hillier, Robin.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Carpi, S, Conti, R & Hillier, R 2013, 'Conformal nets and KK-theory', *Annals of Functional Analysis*, vol. 4, no. 1, pp. 11-17. <http://www.emis.de/journals/AFA/>

Carpi, S., Conti, R., & Hillier, R. (2013). Conformal nets and KK-theory. *Annals of Functional Analysis*, *4*(1), 11-17. http://www.emis.de/journals/AFA/

Carpi S, Conti R, Hillier R. Conformal nets and KK-theory. Annals of Functional Analysis. 2013 Jan;4(1):11-17.

@article{9bfb980a0f984936bd0433415945ff28,

title = "Conformal nets and KK-theory",

abstract = "Given a completely rational conformal net A on S1, its fusion ring acts faithfully on the K-group K0(KA) of a certain universal C-algebra KA associated to A, as shown in a previous paper. We prove here that this action can actually be identied with a Kasparov product, thus paving the way for a fruitful interplay between conformal eld theory and KK-theory.",

keywords = "Operator algebra, conformal field theory, conformal net, superselection sector, fusion ring, K-theory, Kasparov product",

author = "Sebastiano Carpi and Roberto Conti and Robin Hillier",

year = "2013",

month = jan,

language = "English",

volume = "4",

pages = "11--17",

journal = "Annals of Functional Analysis",

issn = "2008-8752",

publisher = "Tusi Mathematical Research Group",

number = "1",

}

TY - JOUR

T1 - Conformal nets and KK-theory

AU - Carpi, Sebastiano

AU - Conti, Roberto

AU - Hillier, Robin

PY - 2013/1

Y1 - 2013/1

N2 - Given a completely rational conformal net A on S1, its fusion ring acts faithfully on the K-group K0(KA) of a certain universal C-algebra KA associated to A, as shown in a previous paper. We prove here that this action can actually be identied with a Kasparov product, thus paving the way for a fruitful interplay between conformal eld theory and KK-theory.

AB - Given a completely rational conformal net A on S1, its fusion ring acts faithfully on the K-group K0(KA) of a certain universal C-algebra KA associated to A, as shown in a previous paper. We prove here that this action can actually be identied with a Kasparov product, thus paving the way for a fruitful interplay between conformal eld theory and KK-theory.

KW - Operator algebra

KW - conformal field theory

KW - conformal net

KW - superselection sector

KW - fusion ring

KW - K-theory

KW - Kasparov product

M3 - Journal article

VL - 4

SP - 11

EP - 17

JO - Annals of Functional Analysis

JF - Annals of Functional Analysis

SN - 2008-8752

IS - 1

ER -