Non-Commutative T-Duality

TL;DR

This paper develops a duality theory for bundles of C*-algebras with fibers as twisted transformation group algebras, generalizing classical T-duality to non-commutative settings and including previous non-commutative T-dual models.

Contribution

It introduces a unified duality framework for bundles of C*-algebras with twisted fibers, extending classical T-duality to non-commutative cases and encompassing prior non-commutative models.

Findings

Established a duality theory for bundles of twisted transformation group C*-algebras.

Generalized classical T-duality to non-commutative fiber bundles.

Included models with twisted group algebras as special cases.

Abstract

A duality theory of bundles of C$^*$-algebras whose fibres are twisted transformation group algebras is established. Classical T-duality is obtained as a special case, where all fibres are commutative tori, i.e. untwisted group algebras for $\Z^n$. Our theory also includes the bundles considered by Mathai and Rosenberg in their work on non-commutative T-duals, in which they allow twisted group algebras on one side of the duality.