# 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.

#### 11 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… Expand

Tracing cyclic homology pairings under twisting of graded algebras

- Mathematics
- Letters 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… Expand

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… Expand

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… Expand

Deformations of Fell bundles and twisted graph algebras

- 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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

Deformation of Spectral Triples and Their Quantum Isometry Groups

- Mathematics
- 2016

This chapter deals with \( \mathrm{QISO}^{\mathcal{L}} \) and \( \mathrm{QISO}^{+}_R \) of a cocycle twisted noncommutative manifold. We first discuss the cocycle deformation of compact quantum… Expand

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