Related papers: Rieffel deformation of group coactions

Let H be a closed subgroup of a locally compact group G and let X=G/H be the quotient space of left cosets. Let C*X be the corresponding G-C*-algebra of continuous functions on X, vanishing at infinity. Suppose that L is a closed abelian…

We show that Rieffel's deformation sends covariant C(T)-algebras into C(T)-algebras. We also treat the lower semi-continuity issue, proving that Rieffel's deformation transforms covariant continuous fields of C*-algebras into continuous…

We start from Rieffel data (A,f,X) where A is a C*-algebra, X is an action of an abelian group H on A and f is a 2-cocycle on the dual group. Using Landstad theory of crossed product we get a deformed C*-algebra A(f). In the case of H being…

In this paper we apply Rieffel deformation to C*- tensor product viewed as a functor on the category of C*-algebras with an abelian group action. In the case of the Rieffel deformation of a quantum group with the action by automorphisms the…

In this paper we consider C*-algebraic deformations a la Rieffel and show that every state of the undeformed algebra can be deformed into a state of the deformed algebra in the sense of a continuous field of states. The construction is…

The main objective of this article is to develop the theory of deformation of $C^*$-algebras endowed with a group action, from the perspective of non-formal equivariant quantization. This program, initiated in \cite{Bieliavsky-Gayral}, aims…

Given a C*-algebra A with a left action of a locally compact quantum group G on it and a unitary 2-cocycle Omega on \hat G, we define a deformation A_Omega of A. The construction behaves well under certain additional technical assumptions…

We revisit the procedure of deformation of $C^*$-algebras via coactions of locally compact groups and extend the methods to cover deformations for maximal, reduced, and exotic coactions for a given group $G$ and circle-valued Borel…

We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of R^d. However, the method used here differs from Rieffel's one: we obtain a Universal…

We develop a deformation framework for $C^*$-algebras equipped with a coaction of a locally compact quantum group, formulated intrinsically at the level of spectral subspaces determined by the coaction. The construction is defined…

In this article we present a new C*-algebraic deformation of the Lorentz group. It is obtained by means of the Rieffel deformation applied to SL(2,C). We give a detailed description of the resulting quantum group in terms of generators -…

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 define a deformation A_\omega of A.…

Any deformation of a Weyl or Clifford algebra can be realized through a change of generators in the undeformed algebra. q-Deformations of Weyl or Clifford algebrae that were covariant under the action of a simple Lie algebra g are…

This paper explores a novel approach to the deformation of $C^*$-algebras via coactions of locally compact groups, emphasizing Fischer's construction in the context of maximal coactions. We establish a rigorous framework for understanding…

Any deformation of a Weyl or Clifford algebra can be realized through some change of generators in the undeformed algebra. Here we briefly describe and motivate our systematic procedure for constructing all such changes of generators for…

In this paper we study deformations of $C^*$-algebras that are given as cross-sectional $C^*$-algebras of Fell bundles over locally compact groups $G$. Our deformation comes from a direct deformation of the Fell bundles via certain…

Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations…

Any deformation of a Weyl or Clifford algebra A can be realized through a `deforming map', i.e. a formal change of generators in A. This is true in particular if A is covariant under a Lie algebra g and its deformation is induced by some…

We review recent works concerning deformation quantization of abelian supergroups. Indeed, we expose the construction of an induced representation of the Heisenberg supergroup and an associated pseudodifferential calculus by using…

We construct a deformation of the quantum algebra Fun(T^*G) associated with Lie group G to the case where G is replaced by a quantum group G_q which has a bicovariant calculus. The deformation easily allows for the inclusion of the current…