Enveloping algebras of preLie algebras, Solomon idempotents and the Magnus formula

Abstract : 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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Submitted on : Tuesday, January 10, 2012 - 1:09:05 PM
Last modification on : Wednesday, December 12, 2018 - 3:21:49 PM
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  • HAL Id : hal-00658228, version 2
  • ARXIV : 1201.2159

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Frédéric Chapoton, Frédéric Patras. Enveloping algebras of preLie algebras, Solomon idempotents and the Magnus formula. International Journal of Algebra and Computation, World Scientific Publishing, 2013, 23 (4), pp.853. ⟨hal-00658228v2⟩

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