Six-Term Exact Sequences for Smooth Generalized Crossed Products
K-Theory and Homology
2011-11-10 v1 Operator Algebras
Abstract
We define smooth generalized crossed products and prove six-term exact sequences of Pimsner-Voiculescu type. This sequence may, in particular, be applied to smooth subalgebras of the Quantum Heisenberg Manifolds in order to compute the generators of their cyclic cohomology. Our proof is based on a combination of arguments from the setting of (Cuntz-)Pimsner algebras and the Toeplitz proof of Bott-periodicity.
Keywords
Cite
@article{arxiv.1111.2154,
title = {Six-Term Exact Sequences for Smooth Generalized Crossed Products},
author = {Olivier Gabriel and Martin Grensing},
journal= {arXiv preprint arXiv:1111.2154},
year = {2011}
}
Comments
This paper is closely related to arXiv:1011.6238v1 [math.KT]. We follow the same general line of argument, but the proofs of this second paper are very different (and simpler). However, the domain of application of the first article is larger and we should rely on this greater generality in future work