Quantum differential calculus

In quantum geometry or noncommutative geometry a quantum differential calculus or noncommutative differential structure on an algebra A {\displaystyle A} over a field k {\displaystyle k} means the specification of a space of differential forms over the algebra. The algebra A {\displaystyle A} here is regarded as a coordinate ring but it is important that it may be noncommutative and hence not an actual algebra of coordinate functions on any actual space, so this represents a point of view replacing the specification of a differentiable structure for an actual space.

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