My understanding is that this is roughly the jumping off point of noncommutative geometry. There has also been recent work which is more algebraic in spirit than the main body of noncommutative geometry, which tends to be functional analysis. For one entry point, see the paper
- William Crawley-Boevey, Pavel Etingof, Victor Ginzburg, Noncommutative geometry and quiver algebras, Advances in Mathematics 209 Issue 1 (2007) pp 274–336, doi:10.1016/j.aim.2006.05.004, arXiv:math/0502301
