H-"aquivariante Morita-"Aquivalenz und Deformationsquantisierung

English abstract: This work contains of five chapters: The first one deals with Morita equivalence of star algebras. In particular star algebras which are equipped with a symmetry given by a Hopf (star-) algebra. In the second chapter we describe the equivariant Picard group and the equivariant Picard groupoid, which are a direct consequence of the results from the first chapter. We calculated the kernel and the image of the groupoid morphism from the equivariant Picard groupoid into the normal one. We give furthermore a formalized version of Morita invariance: given by a functor from the Picard groupoid to another category. This is shown for several examples. In the third chapter we show the connection between Hopf equivariant Morita equivalence of star algebras and the Morita equivalence of cross-product algebras. The forth chapter deals with deformation quantization and gives an extended introduction to (invariant) star products. In the fifth chapter we show the Hopf equivariance of deformed algebras (i.e. of hermitian star products). This is a important examples which concludes the previous chapters.

💡 Research Summary

This paper develops a comprehensive theory of Morita equivalence for star‑algebras equipped with a symmetry given by a Hopf (★)‑algebra, and connects this framework to deformation quantization, especially Hermitian star products. The work is organized into five chapters, each building on the previous results.

Chapter 1 establishes the notion of Hopf‑equivariant Morita equivalence. A star‑algebra A (a ℂ