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| HAL : hal-00685397, version 1 |
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| Some examples of trace-positive quaternary quartics |
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| Ronan Quarez 1 |
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| (05/04/2012) |
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| We give some examples of trace-positive non-commutative quaternary quartics which are not cyclically equivalent to a sum of hermitian squares. Since some similar examples of ternary sextics were already known, this settles a perfect analogy to Hilbert's results from the commutative context which says that in general, positive (commutative) polynomials are not necessarily sums of squares, the first non trivial cases being obtained for ternary sextics and quaternary quartics. |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Géométrie algébrique réelle |
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| Domaine | : | Mathématiques/Géométrie algébrique |
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| Positive semi-definite – Sums of squares – Sums of Hermitian Squares – Trace positivity |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00685397, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00685397 | |
| oai:hal.archives-ouvertes.fr:hal-00685397 | |
| Contributeur : Ronan Quarez | |
| Soumis le : Jeudi 5 Avril 2012, 09:03:39 | |
| Dernière modification le : Jeudi 5 Avril 2012, 13:58:17 | |
