Geodesic
Noncommutative Structures
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and singularities. Part 2, Tome 259 (2007), pp. 203-242

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We propose a method for constructing noncommutative analogs of objects from classical calculus, differential geometry, topology, dynamical systems, etc. The standard (commutative) objects can be obtained from noncommutative ones by natural projections (a set of canonical homomorphisms). The approach is ideologically close to the noncommutative geometry of A. Connes but differs from it in technical details. 
@article{TM_2007_259_a12,
     author = {D. V. Treschev},
     title = {Noncommutative {Structures}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {203--242},
     publisher = {mathdoc},
     volume = {259},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2007_259_a12/}
}
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D. V. Treschev. Noncommutative Structures. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and singularities. Part 2, Tome 259 (2007), pp. 203-242. http://geodesic.mathdoc.fr/item/TM_2007_259_a12/