ENVELOPING ALGEBRAS OF PRELIE ALGEBRAS, SOLOMON IDEMPOTENTS AND THE MAGNUS FORMULA

被引:19
|
作者
Chapoton, Frederic [1 ]
Patras, Frederic [2 ]
机构
[1] Univ Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France
[2] Univ Nice, CNRS, UMR 7351, F-06108 Nice 02, France
关键词
Enveloping algebra; preLie algebra; Lie idempotents; Poincare-Birkhoff-Witt; Magnus formula; HOPF-ALGEBRAS; TREES;
D O I
10.1142/S0218196713400134
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the internal structure of enveloping algebras of preLie algebras. We show in particular that the canonical projections arising from the Poincare-Birkhoff-Witt theorem can be computed explicitly. 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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页码:853 / 861
页数:9
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