On deformations of C*-algebras by actions of Kahlerian Lie groups

TL;DR

This paper demonstrates the equivalence of two methods for equivariant strict deformation quantization of C*-algebras using actions of negatively curved Kahlerian Lie groups, one via oscillatory integrals and the other via dual 2-cocycles.

Contribution

It establishes the equivalence between two distinct approaches to deformation quantization for C*-algebras under Kahlerian Lie group actions.

Findings

Both approaches are mathematically equivalent.

The methods unify the understanding of deformation quantization in this context.

Provides a foundation for further research in quantum group actions.

Abstract

We show that two approaches to equivariant strict deformation quantization of C*-algebras by actions of negatively curved Kahlerian Lie groups, one based on oscillatory integrals and the other on quantizations maps defined by dual 2-cocycles, are equivalent.