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2013 Conformal Nets and KK-Theory
Sebastiano Carpi, Roberto Conti, Robin Hillier
Ann. Funct. Anal. 4(1): 11-17 (2013). DOI: 10.15352/afa/1399899832


‎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.


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Sebastiano Carpi. Roberto Conti. Robin Hillier. "Conformal Nets and KK-Theory." Ann. Funct. Anal. 4 (1) 11 - 17, 2013.


Published: 2013
First available in Project Euclid: 12 May 2014

zbMATH: 1266.81138
MathSciNet: MR3004206
Digital Object Identifier: 10.15352/afa/1399899832

Primary: 81Txx
Secondary: 19K35 , 46Lxx‎ , 58B34

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

Rights: Copyright © 2013 Tusi Mathematical Research Group

Vol.4 • No. 1 • 2013
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