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Lie Theory and Its Applications in Physics pp 95–107Cite as

Exponential Series Without Denominators

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 36))

Abstract

For a commutative algebra which comes from a Zinbiel algebra the exponential series can be written without denominators. When lifted to dendriform algebras this new series satisfies a functional equation analogous to the Baker-Campbell-Hausdorff formula. We make it explicit by showing that the obstruction series is the sum of the brace products. In the multilinear case we show that the role the Eulerian idempotent is played by the iterated pre-Lie product.

Professor Jean-Louis Loday passed away on 6 June 2012.

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References

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Acknowledgements

This work was partially supported by the French-Bulgarian project RILA under the contract Egide-Rila N112.

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Authors and Affiliations

  1. Institut de Recherche Mathématique Avancée, CNRS et Université de Strasbourg, Zinbiel Institute of Mathematics, Strasbourg, France

    Jean-Louis Loday

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  1. Jean-Louis Loday
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Editors and Affiliations

  1. Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, Sofia, 1784, Sofiya, Bulgaria

    Vladimir Dobrev

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Loday, JL. (2013). Exponential Series Without Denominators. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 36. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54270-4_7

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