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Posetted Trees and Baker-Campbell-Hausdorff Product

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Abstract

In this paper, we use some typical tools of algebraic operads and homotopy transfer theory, in order to give a simple and elementary combinatorial description of the Baker-Campbell-Hausdorff formula. More precisely, we exploit the usual operadic notion of planar rooted trees, enriched with the notion of subroots, and we define a posetted tree as a planar rooted tree endowed with a monotone labelling of leaves, with elements in a partially ordered set. The main result of this paper is an explicit expression of the Baker-Campbell-Hausdorff product as a sum of iterated brackets over an indexing set of posetted binary trees.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, I-70125, Bari, Italy

    Donatella Iacono

  2. Dipartimento di Matematica “Guido Castelnuovo”, Università degli Studi di Roma La Sapienza, P.le Aldo Moro 5, I-00185, Roma, Italy

    Marco Manetti

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  1. Donatella Iacono
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  2. Marco Manetti
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Correspondence to Donatella Iacono.

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Iacono, D., Manetti, M. Posetted Trees and Baker-Campbell-Hausdorff Product. Mediterr. J. Math. 10, 611–623 (2013). https://doi.org/10.1007/s00009-012-0235-z

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  • DOI: https://doi.org/10.1007/s00009-012-0235-z

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