• 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. 
Monodromy of the Gauss-Manin connection for deformation by group cocycles
We consider the 2-cocycle deformation of algebras graded by discrete groups. The action of the Maurer-Cartan form on cyclic cohomology is shown to be cohomologous to the cup product action of the
Tracing cyclic homology pairings under twisting of graded algebras
We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the
TRAC ING CYCL IC HOMOLOGY PA IR INGS UNDER TW IST ING OF GRADED ALGEBRAS
We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the
Crossed Product Equivalence of Quantum Automorphism Groups
We compare algebras of the quantum automorphism group of finite-dimensional C∗-algebra B and the quantum permutation group S N , where N = dimB. We show that matrix amplification and crossed products
Deformations of Fell bundles and twisted graph algebras
  • I. Raeburn
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2016
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
Compact Lie group actions with continuous Rokhlin property
In this paper, we study continuous Rokhlin property of $\mathrm{C}^*$-dynamical systems using techniques of equivariant $\mathrm{KK}$-theory and quantum group theory. In particular, we determine the
Duality theory for nonergodic actions
Generalizing work by Pinzari and Roberts, we characterize actions of a compact quantum group G on C*-algebras in terms of what we call weak unitary tensor functors from Rep G into categories of
...
1
2
...

References

SHOWING 1-10 OF 34 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 a
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 shown
Heat kernels and the range of the trace on completions of twisted group algebras
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
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
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
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 of
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 the
...
1
2
3
4
...