Let XX be a space, intended as a possibly curved space–time, and AA a precosheaf of C∗C∗-algebras on XX. Motivated by algebraic quantum field theory, we study the Kasparov and ΘΘ-summable KK-homology of AA interpreting them in terms of the holonomy equivariant KK-homology of the associated C∗C∗-dynamical system. This yields a characteristic class for KK-homology cycles of AA with values in the odd cohomology of XX, that we interpret as a generalized statistical dimension.
Ruzzi, G., Vasselli, E. (2014). The K-homology of nets of C*-algebras. JOURNAL OF GEOMETRY AND PHYSICS, 86, 476-491 [10.1016/j.geomphys.2014.10.003].
The K-homology of nets of C*-algebras
RUZZI, GIUSEPPE;
2014-01-01
Abstract
Let XX be a space, intended as a possibly curved space–time, and AA a precosheaf of C∗C∗-algebras on XX. Motivated by algebraic quantum field theory, we study the Kasparov and ΘΘ-summable KK-homology of AA interpreting them in terms of the holonomy equivariant KK-homology of the associated C∗C∗-dynamical system. This yields a characteristic class for KK-homology cycles of AA with values in the odd cohomology of XX, that we interpret as a generalized statistical dimension.| File | Dimensione | Formato | |
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