### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 041, 12 pages      arXiv:1612.03559      https://doi.org/10.3842/SIGMA.2017.041

### Non-Commutative Vector Bundles for Non-Unital Algebras

School of Mathematics and Applied Statistics, University of Wollongong, Northfields Ave 2522, Australia

Received December 13, 2016, in final form June 12, 2017; Published online June 16, 2017

Abstract
We revisit the characterisation of modules over non-unital $C^*$-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.

Key words: Hilbert module; vector bundle; multiplier module; Watatani index.

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