Bongaarts, P. J. M.; Pijls, H. G. J. Almost commutative algebra and differential calculus on the quantum hyperplane. (English) Zbl 0808.17011 J. Math. Phys. 35, No. 2, 959-970 (1994). 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. Cited in 1 ReviewCited in 11 Documents 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 Keywords:de Rham complex; Poisson structure; quantum groups; almost commutative algebra; differential calculus; quantum hyperplane PDF BibTeX XML Cite \textit{P. J. M. Bongaarts} and \textit{H. G. J. Pijls}, J. Math. Phys. 35, No. 2, 959--970 (1994; Zbl 0808.17011) Full Text: DOI Link OpenURL References: [1] Connes A., Publ. Math. IHES 62 pp 257– (1986) [2] Martin J. L., Proc. R. Soc. London, Ser. A 251 pp 561– (1959) [3] DOI: 10.1073/pnas.48.4.603 · Zbl 0116.45002 [4] DOI: 10.1070/RM1980v035n01ABEH001545 · Zbl 0462.58002 [5] DOI: 10.1063/1.526780 [6] DOI: 10.1016/0920-5632(91)90143-3 [7] DOI: 10.1016/0370-2693(91)90801-V [8] DOI: 10.1007/BF01219077 · Zbl 0627.58034 [9] DOI: 10.1007/BF02099136 · Zbl 0734.60048 [10] DOI: 10.1007/BF01221411 · Zbl 0751.58042 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.