The theory of algebraic varieties gives an algebraic interpretation of differential geometry, thus of our physical world. To treat, among other physical properties, the theory of entanglement, we need to generalize the space parametrizing the objects of physics. We do this by introducing noncommutative varieties.
"Physical Interpretation of Noncommutative Algebraic Varieties." J. Phys. Math. 6 (1) 1 - 3, 2015. https://doi.org/10.4172/2090-0902.1000132