# 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…

## 5 Citations

### Representations of *-algebras by unbounded operators: C*-hulls, local-global principle, and induction

- Mathematics
- 2016

We define a C*-hull for a *-algebra, given a notion of integrability for its representations on Hilbert modules. We establish a local-global principle which, in many cases, characterises integrable…

### Aperiodicity, topological freeness and pure outerness: From group actions to Fell bundles

- Mathematics
- 2016

We generalise various non-triviality conditions for group actions to Fell bundles over discrete groups and prove several implications between them. We also study sufficient criteria for the reduced…

### Symmetry and spectral invariance for topologically graded C∗$C^*$ ‐algebras and partial action systems

- MathematicsBulletin of the London Mathematical Society
- 2022

A discrete group G${\sf G}$ is called rigidly symmetric if the projective tensor product between the convolution algebra ℓ1(G)$\ell ^1({\sf G})$ and any C∗$C^*$ ‐algebra A$\mathcal {A}$ is symmetric.…

### A Fejér theorem for boundary quotients arising from algebraic dynamical systems

- Mathematics
- 2019

A Fejer-type theorem is proved within the framework of $C^*$-algebras associated with certain irreversible algebraic dynamical systems. This makes it possible to strengthen a result on the structure…

### ON GRADED $C^{\ast }$ -ALGEBRAS

- MathematicsBulletin of the Australian Mathematical Society
- 2017

We show that every topological grading of a $C^{\ast }$ -algebra by a discrete abelian group is implemented by an action of the compact dual group.

## 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…