It is proven that every flat connection or covariant derivative ∇ on a left A-module M (with respect to the universal differential calculus) induces a right A-module structure on M so that ∇ is a bimodule connection on M or M is a flat differentiable bimodule. Similarly a flat hom-connection on a right A-module M induces a compatible left A-action.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-2,
author = {Tomasz Brzezi\'nski},
title = {A note on flat noncommutative connections},
journal = {Banach Center Publications},
volume = {97},
year = {2012},
pages = {43-53},
zbl = {1272.58004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-2}
}
Tomasz Brzeziński. A note on flat noncommutative connections. Banach Center Publications, Tome 97 (2012) pp. 43-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-2/