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.


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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