Non-Commutative Vector Bundles for Non-Unital Algebras

Abstract

We revisit the characterisation of modules over non-unital $C^{\ast }$-algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier module characterises a class of modules which closely mirror the commutative case. We also investigate the multiplier-module construction in the context of bi-Hilbertian bimodules, particularly those of finite numerical index and finite Watatani index.

Cited by in corpus (2)

• The Cayley transform in complex, real and graded $K$-theory
• Poincare duality for Cuntz-Pimsner algebras of bimodules