Noncommutative projective geometry

Noncommutative projective geometry is a branch of mathematics that extends the concepts of projective geometry into the realm of noncommutative algebra. In classical projective geometry, we deal with geometric objects and relationships in a way that relies on commutative algebra, primarily over fields. However, in noncommutative projective geometry, we consider spaces and structures where the coordinates do not commute, often inspired by physics, particularly quantum mechanics and string theory.