Deformation of algebras associated to group cocycles
@article{Yamashita2011DeformationOA, title={Deformation of algebras associated to group cocycles}, author={Makoto Yamashita}, journal={arXiv: Operator Algebras}, year={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 cocycles which can be perturbed to the trivial one.
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References
SHOWING 1-10 OF 34 REFERENCES
K-groups of C*-algebras deformed by actions of Rd
- Mathematics
- 1993
Abstract We show that the topological K -groups of a C *-algebra deformed by an action of R d are isomorphic to those of the original C *-a1gebra. We do this by exhibiting the deformed algebra as a…
Connes–Landi Deformation of Spectral Triples
- Mathematics
- 2010
We describe a way to deform a spectral triple with a 2-torus action parametrized by a real deformation parameter, motivated by the Connes–Landi deformation of manifolds. Such deformations are shown…
Heat kernels and the range of the trace on completions of twisted group algebras
- Mathematics
- 2006
Heat kernels are used in this paper to express the analytic index of projectively invariant Dirac type operators on G-covering spaces of compact manifolds, as elements in the K-theory of certain…
Properties preserved under Morita equivalence of C*-algebras
- Mathematics
- 2005
We show that important structural properties of C*-algebras and the multiplicity numbers of representations are preserved under Morita equivalence.
K-HOMOLOGY CLASS OF THE DIRAC OPERATOR ON A COMPACT QUANTUM GROUP
- Mathematics
- 2011
By a result of Nagy, the C � -algebra of continuous func- tions on the q-deformation Gq of a simply connected semisimple com- pact Lie group G is KK-equivalent to C(G). We show that under this…
Amenability and exactness for dynamical systems and their C*-algebras
- Mathematics
- 2000
We study the relations between amenability (resp. amenability at infinity) of C*-dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.
The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ)
- Mathematics
- 2006
Abstract Let F ⊆ SL2(ℤ) be a finite subgroup (necessarily isomorphic to one of ℤ2, ℤ3, ℤ4, or ℤ6), and let F act on the irrational rotational algebra Aθ via the restriction of the canonical action of…
Twisted crossed products of C *-algebras
- Mathematics
- 1989
Group algebras and crossed products have always played an important role in the theory of C *-algebras, and there has also been considerable interest in various twisted analogues, where the…