The Hopf Algebra of Rooted Trees, Free Lie Algebras, and Lie Series

We present an approach that allows performing computations related to the Baker-Campbell-Haussdorff (BCH) formula and its generalizations in an arbitrary Hall basis, using labeled rooted trees. In particular, we provide explicit formulas (given in terms of the structure of certain labeled rooted trees) of the continuous BCH formula. We develop a rewriting algorithm (based on labeled rooted trees) in the dual Poincar

• Type: Journal
• Year: 2006
• Where: FOCM
• Authors: A. Murua
• Keywords: Arbitrary Hall, Arbitrary Hall Basis, FOCM 2006, Lie Series