## Almost commutative algebra and differential calculus on the quantum hyperplane.(English)Zbl 0808.17011

Summary: A notion of almost commutative algebra is given that makes it possible to extend differential geometric ideas associated with commutative algebras in a simple manner to certain classes of noncommutative algebras. As an example a differential calculus on the $$N$$-dimensional quantum hyperplane is discussed.

### MSC:

 17B37 Quantum groups (quantized enveloping algebras) and related deformations 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 46L87 Noncommutative differential geometry
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### References:

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