Deformations of Fell bundles and twisted graph algebras
@article{Raeburn2016DeformationsOF,
title={Deformations of Fell bundles and twisted graph algebras},
author={Iain Raeburn},
journal={Mathematical Proceedings of the Cambridge Philosophical Society},
year={2016},
volume={161},
pages={535 - 558}
}Abstract We consider Fell bundles over discrete groups, and the C*-algebra which is universal for representations of the bundle. We define deformations of Fell bundles, which are new Fell bundles with the same underlying Banach bundle but with the multiplication deformed by a two-cocycle on the group. Every graph algebra can be viewed as the C*-algebra of a Fell bundle, and there are many cocycles of interest with which to deform them. We thus obtain many of the twisted graph algebras of…
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References
SHOWING 1-10 OF 50 REFERENCES
On the structure of twisted group C*-algebras
- Mathematics
- 1992
We first give general structural results for the twisted group algebras C*(G, σ) of a locally compact group G with large abelian subgroups. In particular, we use a theorem of Williams to realise…
Coverings of Directed Graphs and Crossed Products of C*-Algebras by Coactions of Homogeneous Spaces
- Mathematics
- 2002
We show that if p:F→E is a covering of directed graphs, then the Cuntz–Krieger algebra C*(F) of F can be viewed as a crossed product of C*(E) by a coaction of a homogeneous space for the fundamental…
Co-universal C*-algebras associated to generalised graphs
- Mathematics
- 2010
We introduce P-graphs, which are generalisations of directed graphs in which paths have a degree in a semigroup P rather than a length in ℕ. We focus on semigroups P arising as part of a…
Representations of crossed products by coactions and principal bundles
- Mathematics
- 1987
Abstract The main purpose of this paper is to establish a covariant representation theory for coactions of locally compact groups on C * -algebras (including a notion of exterior equivalence), to…
Higher Rank Graph C-Algebras
- Mathematics
- 2000
Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that of…
Deformation of algebras associated to group cocycles
- Mathematics
- 2011
We define a deformation of algebras endowed with coaction of the reduced group algebras. The deformation parameter is given by a 2-cocycle over the group. We prove K-theory isomorphisms for the…