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| HAL : hal-00658228, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (10-01-2012) | v2 (10-01-2012) |
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| Enveloping algebras of preLie algebras, Solomon idempotents and the Magnus formula |
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| Frédéric Chapoton 1Frédéric Patras 2 |
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| (10/01/2012) |
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| We study the internal structure of enveloping algebras of preLie algebras. We show in particular that the canonical projections arising from the Poincaré-Birkhoff-Witt theorem can be computed explicitely. They happen to be closely related to the Magnus formula for matrix differential equations. Indeed, we show that the Magnus formula provides a way to compute the canonical projection on the preLie algebra. Conversely, our results provide new insights on classical problems in the theory of differential equations and on recent advances in their combinatorial understanding. |
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| 1 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| 2 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] |
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| Domaine | : | Mathématiques/Algèbres quantiques |
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| enveloping algebra – Lie idempotent – preLie algebra – Magnus formula |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00658228, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00658228 | |
| oai:hal.archives-ouvertes.fr:hal-00658228 | |
| Contributeur : Frédéric Chapoton | |
| Soumis le : Mardi 10 Janvier 2012, 10:33:08 | |
| Dernière modification le : Mardi 10 Janvier 2012, 11:47:45 | |
