# 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.

## 12 Citations

Monodromy of the Gauss-Manin connection for deformation by group cocycles

- Mathematics
- 2012

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

- MathematicsLetters in Mathematical Physics
- 2019

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

- 2017

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…

Compact Lie group action with the continuous Rokhlin property

- Mathematics
- 2017

Abstract In this paper, we study the continuous Rokhlin property of C ⁎ -dynamical systems using techniques of equivariant KK-theory and quantum group theory. In particular, we determine the…

Deformations of Fell bundles and twisted graph algebras

- MathematicsMathematical 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…

Deformation of operator algebras by Borel cocycles

- Mathematics
- 2012

Assume that we are given a coaction \delta of a locally compact group G on a C*-algebra A and a T-valued Borel 2-cocycle \omega on G. Motivated by the approach of Kasprzak to Rieffel's deformation we…

Compact Lie group actions with continuous Rokhlin property

- Mathematics
- 2015

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…

Deformation of C⁎-algebras by cocycles on locally compact quantum groups

- Mathematics
- 2013

Given a C⁎-algebra A with a left action of a locally compact quantum group G on it and a unitary 2-cocycle Ω on Gˆ, we define a deformation AΩ of A. The construction behaves well under certain…

Duality theory for nonergodic actions

- Mathematics
- 2013

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…

Projective representation theory for compact quantum groups and the quantum Baum-Connes assembly map

- Mathematics
- 2021

We study the theory of projective representations for a compact quantum group G, i.e. actions of G on BpHq for some Hilbert space H. We show that any such projective representation is inner, and is…

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