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

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For 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.
19 pages. To appear Seminaire Lotharingien de Combinatoire: http://www.mat.univie.ac.at/~slc/

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Combinatorics, Symbolic Computation, Differential Geometry, 53B20, 15A72, 05E10, 16D60, 05-04

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http://salesiana.dossiersoluciones.com/handle/123456789/66048

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0212278
 http://arxiv.org/abs/math/0212278
 Seminaire Lotharingien de Combinatoire, 48 (2003) Article B48d

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arXiv