Classification of differentials on quantum doubles and finite noncommutative geometry

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dc.creatorMajid, S.
dc.date2002-05-14
dc.date2003-10-09
dc.date.accessioned2026-07-07T04:48:29Z
dc.date.available2026-07-07T04:48:29Z
dc.descriptionWe discuss the construction of finite noncommutative geometries on Hopf algebras and finite groups in the `quantum groups approach'. We apply the author's previous classification theorem, implying that calculi in the factorisable case correspond to blocks in the dual, to classify differential calculi on the quantum codouble $D^*(G)=kG\lcocross k(G)$ of a finite group $G$. We give $D^*(S_3)$ as an example including its exterior algebra and lower cohomology. We also study the calculus on $D^*(\CA)$ induced from one on a general Hopf algebra $\CA$ in general and specialise to $D^*(G)=U(\cg)\lcocross k[G]$ as a noncommutative isometry group of an enveloping algebra $U(\cg)$ as a noncommutative space.
dc.descriptionFinal version to be published Marcel Dekker Lect. Notes Pure Appl. Maths; added final section with calculus on quantum double of a general Hopf algebra. 21 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0205150
dc.identifierhttp://arxiv.org/abs/math/0205150
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64067
dc.subjectQuantum Algebra
dc.subjectDifferential Geometry
dc.subject58B32, 58B34, 20C05
dc.titleClassification of differentials on quantum doubles and finite noncommutative geometry
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