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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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[3] DOI: 10.1073/pnas.48.4.603 · Zbl 0116.45002 · doi:10.1073/pnas.48.4.603
[4] DOI: 10.1070/RM1980v035n01ABEH001545 · Zbl 0462.58002 · doi:10.1070/RM1980v035n01ABEH001545
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