Corpus ID: 117038447

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}
}
  • M. Yamashita
  • Published 13 July 2011
  • Mathematics
  • arXiv: Operator Algebras
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 16 REFERENCES
K-groups of C*-algebras deformed by actions of Rd
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 aExpand
Connes–Landi Deformation of Spectral Triples
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 shownExpand
Equivariant Poincaré duality for quantum group actions
We extend the notion of Poincare duality in KK-theory to the setting of quantum group actions. An important ingredient in our approach is the replacement of ordinary tensor products by braided tensorExpand
K-HOMOLOGY CLASS OF THE DIRAC OPERATOR ON A COMPACT QUANTUM GROUP
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 thisExpand
Amenability and exactness for dynamical systems and their C*-algebras
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)
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 ofExpand
Twisted crossed products of C *-algebras
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 theExpand
Quantized Algebras of Functions on Homogeneous Spaces with Poisson Stabilizers
Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0 < q < 1. We study a quantization C(Gq/Kq) of the algebra of continuousExpand
The Baum-Connes conjecture via localisation of categories
Abstract We redefine the Baum–Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and givesExpand
Deformation quantization of Heisenberg manifolds
ForM a smooth manifold equipped with a Poisson bracket, we formulate aC*-algebra framework for deformation quantization, including the possibility of invariance under a Lie group of diffeomorphismsExpand
...
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