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The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor

Carminati, John and Lim, Allan 2006, The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor, Journal of mathematical physics, vol. 47, no. 5, pp. 052504-1-052504-24.

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Title The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor
Author(s) Carminati, John
Lim, Allan
Journal name Journal of mathematical physics
Volume number 47
Issue number 5
Start page 052504-1
End page 052504-24
Publisher American Institute of Physics
Place of publication New York, N. Y.
Publication date 2006-05
ISSN 0022-2488
1089-7658
Keyword(s) polynomial invariants
constructive graph-theoretic methods
polynomials
Riemann tensor
Summary We continue our analysis of the polynomial invariants of the Riemann tensor in a four-dimensional Lorentzian space. We concentrate on the mixed invariants of even degree in the Ricci spinor Φ<sub>ABȦḂ</sub> and show how, using constructive graph-theoretic methods, arbitrary scalar contractions between copies of the Weyl spinor ψ<sub>ABCD</sub>, its conjugate ψ<sub>ȦḂĊḊ</sub> and an even number of Ricci spinors can be expressed in terms of paired contractions between these spinors. This leads to an algorithm for the explicit expression of dependent invariants as polynomials of members of the complete set. Finally, we rigorously prove that the complete set as given by Sneddon [J. Math. Phys. 39, 1659-1679 (1998)] for this case is both complete and minimal.
Language eng
Field of Research 010102 Algebraic and Differential Geometry
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2006, American Institute of Physics
Persistent URL http://hdl.handle.net/10536/DRO/DU:30003846

Document type: Journal Article
Collection: School of Engineering and Information Technology
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