Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 091, 12 pages      arXiv:1101.2751      https://doi.org/10.3842/SIGMA.2012.091

Covariant Fields of C*-Algebras under Rieffel Deformation

Fabian Belmonte a and Marius Măntoiu b
a) D728, building A, SISSA-ISAS, Via Bonomea 265, 34136 Trieste, Italy
b) Departamento de Matemáticas, Universidad de Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile

Received August 26, 2012, in final form November 22, 2012; Published online November 28, 2012

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.

Key words: pseudodifferential operator; Rieffel deformation; C*-algebra; continuous field; noncommutative dynamical system.

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