My understanding is that this is roughly the jumping off point of [noncommutative geometry][1].  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 of Crawley-Boevey, Etingof and Ginzburg on ["Noncommutative geometry and quiver algebras."][2]

[1]:http://en.wikipedia.org/wiki/Noncommutative_geometry  
[2]:http://front.math.ucdavis.edu/0502.5301