Non-Commutative T-Duality

Abstract

A duality theory of bundles of C${}^{\ast }$-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 ${\mathbb{Z}}^n$. 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.

We extended the introduction and added some more examples. The paper will appear in the New York Journal of Mathematics

References in corpus (3)

• Principal noncommutative torus bundles
• Die lokale Struktur von T-Dualitätstripeln
• Equivariant T-Duality of Locally Compact Abelian Groups