Rieffel's deformation quantization and isospectral deformations. (Q5950971)

\textit{M. A. Rieffel} [Mem. Am. Math. Soc. 506 (1993; Zbl 0798.46053)] studied deformation quantization within the framework of C\(^*\)-algebras. He generalized the ``twisted'' or the ``Moyal product'' using the action of \(\mathbb{R}^d\) on any \(C^*\)-algebra. In the framework of noncommutative geometry \textit{A. Connes} and \textit{G. Landi} [Commun. Math. Phys. 221, 141--159 (2001; Zbl 0997.81045)] have introduced isospectral deformations. In the paper under consideration, Sitarz shows that the isospectral deformations of a rank two isometry group as defined by Connes and Landi are a special case of Rieffel's construction in the same particular example of the noncommutative torus. The calculation is based on a study on symmetries underlying the deformation [\textit{A. Sitarz}, Twisted and spectral triples for isospectral deformations, mathQA/0102074].