# 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.

## 13 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

- Mathematics
- 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…

Crossed Product Equivalence of Quantum Automorphism Groups

- Mathematics
- 2022

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

- 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…

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…

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…

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