Nonassociative strict deformation quantization of C*-algebras and nonassociative torus bundles

Abstract

In this paper, we initiate the study of nonassociative strict deformation quantization of C∗-algebras with a torus action. We shall also present a definition of nonassociative principal torus bundles, and give a classification of these as nonassociative strict deformation quantization of ordinary principal torus bundles. We then relate this to T-duality of principal torus bundles with H-flux. In particular, the Octonions fit nicely into our theory.