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

TL;DR

This paper develops a framework for nonassociative deformation quantization of C*-algebras with torus actions, introduces nonassociative principal torus bundles, and connects these concepts to T-duality and Octonions.

Contribution

It introduces the concept of nonassociative strict deformation quantization and classifies nonassociative principal torus bundles, linking them to T-duality and Octonions.

Findings

Classification of nonassociative principal torus bundles

Relation to T-duality with H-flux

Incorporation of Octonions into the theory

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. We also show that the Octonions fit nicely into our theory.