Determination of the structure of algebraic curvature tensors by means of Young symmetrizers

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dc.creatorFiedler, B.
dc.date2002-12-19
dc.date2002-12-23
dc.date.accessioned2026-07-07T04:53:56Z
dc.date.available2026-07-07T04:53:56Z
dc.descriptionFor a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins that every algebraic curvature tensor has a structure which is very similar to that of the above Osserman curvature tensors. We verify our results by means of the Littlewood-Richardson rule and plethysms. For certain symbolic calculations we used the Mathematica packages MathTensor, Ricci and PERMS.
dc.description19 pages. To appear Seminaire Lotharingien de Combinatoire: http://www.mat.univie.ac.at/~slc/
dc.identifierhttps://arxiv.org/abs/math/0212278
dc.identifierhttp://arxiv.org/abs/math/0212278
dc.identifierSeminaire Lotharingien de Combinatoire, 48 (2003) Article B48d
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66048
dc.subjectCombinatorics
dc.subjectSymbolic Computation
dc.subjectDifferential Geometry
dc.subject53B20, 15A72, 05E10, 16D60, 05-04
dc.titleDetermination of the structure of algebraic curvature tensors by means of Young symmetrizers
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