# The $C(X)$-algebra of a net and index theory

April 30, 2014

Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov K-homology of A, and interpret them in terms, respectively, of the representation theory and the K-homology of the associated C(X)-algebra. When A is an observable net over the spacetime X in the sense of algebraic quantum field theory, this yields a geometric description of the recently discovered representations affected by the topology of X.

open access link
Journal of Functional Analysis 267 (2014) 112–143

@article{Ruzzi:2012wn,
author = "Ruzzi, Giuseppe and Vasselli, Ezio",
title = "{The C(X)-algebra of a net and index theory}",
year = "2012",
eprint = "1212.2801",
archivePrefix = "arXiv",
primaryClass = "math.OA",
SLACcitation = "%%CITATION = ARXIV:1212.2801;%%"
}

Keywords:

Superselection Theory, QFT on curved spacetimes, noncommutative geometry