Generators of algebraic covariant derivative curvature tensors and Young symmetrizers
| dc.creator | Fiedler, B. | |
| dc.date | 2003-10-02 | |
| dc.date.accessioned | 2026-07-07T06:28:47Z | |
| dc.date.available | 2026-07-07T06:28:47Z | |
| dc.description | We show that the space of algebraic covariant derivative curvature tensors R' is generated by Young symmetrized tensor products W*U or U*W, where W and U are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2),(3)}, {(2),(2 1)} or {(1 1),(2 1)}. Each of the partitions (2), (3) and (1 1) describes exactly one symmetry class, whereas the partition (2 1) characterizes an infinite set S of irreducible symmetry classes. This set S contains exactly one symmetry class S_0 whose elements U can not play the role of generators of tensors R'. The tensors U of all other symmetry classes from S\{S_0} can be used as generators for tensors R'. Foundation of our investigations is a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins about a Young symmetrizer that generates the symmetry class of algebraic covariant derivative curvature tensors. Furthermore we apply ideals and idempotents in group rings C[Sr], the Littlewood-Richardson rule and discrete Fourier transforms for symmetric groups Sr. For certain symbolic calculations we used the Mathematica packages Ricci and PERMS. | |
| dc.description | 18 pages. Chapter for a book "Progress in Computer Science Research", in preparation by Nova Science Publishers, Inc.: http://www.novapublishers.com/ | |
| dc.identifier | https://arxiv.org/abs/math/0310020 | |
| dc.identifier | http://arxiv.org/abs/math/0310020 | |
| dc.identifier | In: Leading-Edge Computer Science, S. Shannon (ed.), Nova Science Publishers, Inc. New York, 2006. pp. 219-239. ISBN: 1-59454-526-X | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97818 | |
| dc.subject | Combinatorics | |
| dc.subject | Symbolic Computation | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B20; 15A72; 05E10; 16D60; 05-04 | |
| dc.title | Generators of algebraic covariant derivative curvature tensors and Young symmetrizers | |
| dc.type | text |