Short formulas for algebraic covariant derivative curvature tensors via Algebraic Combinatorics
| dc.creator | Fiedler, Bernd | |
| dc.date | 2003-12-08 | |
| dc.date.accessioned | 2026-07-07T05:03:40Z | |
| dc.date.available | 2026-07-07T05:03:40Z | |
| dc.description | We consider generators of algebraic covariant derivative curvature tensors R' which can be constructed by a Young symmetrization of product tensors W*U or U*W, where W and U are covariant tensors of order 2 and 3. W is a symmetric or alternating tensor whereas U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2,1). Using Computer Algebra we search for such generators whose coordinate representations are polynomials with a minimal number of summands. For a generic choice of the symmetry class of U we obtain lengths of 16 or 20 summands if W is symmetric or skew-symmetric, respectively. In special cases these numbers can be reduced to the minima 12 or 10. If these minima occur then U admits an index commutation symmetry. Furthermore minimal lengths are possible if U is formed from torsion-free covariant derivatives of symmetric or alternating 2-tensor fields. 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[S_r] and discrete Fourier transforms for symmetric groups S_r. For symbolic calculations we used the Mathematica packages Ricci and PERMS. | |
| dc.description | 38 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312171 | |
| dc.identifier | http://arxiv.org/abs/math/0312171 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69516 | |
| dc.subject | Combinatorics | |
| dc.subject | Symbolic Computation | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B20, 15A72, 05E10, 16D60, 05-04 | |
| dc.title | Short formulas for algebraic covariant derivative curvature tensors via Algebraic Combinatorics | |
| dc.type | text |