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

Giuseppe Ruzzi; Ezio Vasselli

doi:10.1016/j.jfa.2014.04.010

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arXiv · 1212.2801

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

Giuseppe Ruzzi·Ezio Vasselli

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Abstract

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.

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BibTeX RIS

Giuseppe Ruzzi, Ezio Vasselli. 2014-04-17. The C(X)-algebra of a net and index theory. https://doi.org/10.1016/j.jfa.2014.04.010

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