Non-Commutative Vector Bundles for Non-Unital Algebras

Symmetry Integrability and Geometry-Methods and Applications

article

Adam RennieAidan Sims¹ 

[1] School of Mathematics and Applied Statistics, University of Wollongong

关键词: Hilbert module;    vector bundle;    multiplier module;    Watatani index;   

DOI  :  10.3842/SIGMA.2017.041

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown