Annals of Functional Analysis

Conformal Nets and KK-Theory

Sebastiano Carpi, Roberto Conti, and Robin Hillier

Full-text: Open access

Abstract

‎Given a completely rational conformal net $\mathcal{A}$ on $S^1$‎, ‎its fusion‎ ‎ring acts faithfully on the K-group $K_0(\mathfrak{K}_{\mathcal{A}})$ of a certain‎ ‎universal $C^*$-algebra $\mathfrak{K}_{\mathcal{A}}$ associated to $\mathcal{A}$‎, ‎as shown in a‎ ‎previous paper‎. ‎We prove here that this action can actually be‎ ‎identified with a Kasparov product‎, ‎thus paving the way for a‎ ‎fruitful interplay between conformal field theory and KK-theory‎.

Article information

Source
Ann. Funct. Anal., Volume 4, Number 1 (2013), 11-17.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399899832

Digital Object Identifier
doi:10.15352/afa/1399899832

Mathematical Reviews number (MathSciNet)
MR3004206

Zentralblatt MATH identifier
1266.81138

Subjects
Primary: 81Txx: Quantum field theory; related classical field theories [See also 70Sxx]
Secondary: 46Lxx‎ ‎58B34‎ 19K35: Kasparov theory ($KK$-theory) [See also 58J22]

Keywords
Operator algebra conformal field theory conformal net superselection sector fusion ring ‎K-theory Kasparov product

Citation

Carpi, Sebastiano; Conti, Roberto; Hillier, Robin. Conformal Nets and KK-Theory. Ann. Funct. Anal. 4 (2013), no. 1, 11--17. doi:10.15352/afa/1399899832. https://projecteuclid.org/euclid.afa/1399899832


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