Covariant Fields of C*-Algebras under Rieffel Deformation

TL;DR

This paper demonstrates that Rieffel's deformation preserves the structure of covariant C(T)-algebras and continuous fields of C*-algebras, with implications for quantum groups and other examples.

Contribution

It establishes that Rieffel's deformation maintains covariant C(T)-algebra structures and the continuity of fields of C*-algebras, addressing semi-continuity issues.

Findings

Rieffel's deformation preserves covariant C(T)-algebras.

Rieffel's deformation transforms covariant continuous fields into continuous fields.

Examples include applications to quantum groups.

Abstract

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 fields of C*-algebras. Some examples are indicated, including certain quantum groups.