A non-associative baker-campbell-hausdorff formula

  1. Mostovoy, J. 1
  2. Pérez-Izquierdo, J.M. 2
  3. Shestakov, I.P. 3
  1. 1 Instituto Politécnico Nacional
    info

    Instituto Politécnico Nacional

    Ciudad de México, México

    ROR https://ror.org/059sp8j34

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  3. 3 Universidade de São Paulo
    info

    Universidade de São Paulo

    São Paulo, Brasil

    ROR https://ror.org/036rp1748

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Revista:
Proceedings of the American Mathematical Society

ISSN: 0002-9939

Año de publicación: 2017

Volumen: 145

Número: 12

Páginas: 5109-5122

Tipo: Artículo

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DOI: 10.1090/PROC/13684 SCOPUS: 2-s2.0-85032915210 WoS: WOS:000414148600009 GOOGLE SCHOLAR

Otras publicaciones en: Proceedings of the American Mathematical Society

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Álgebra y superálgebras de Lie. Teoría de Lie no asociativa

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Resumen

We address the problem of constructing the non-associative version of the Dynkin form of the Baker-Campbell-Hausdorff formula; that is, expressing log(exp(x) exp(y)), where x and y are non-associative variables, in terms of the Shestakov-Umirbaev primitive operations. In particular, we obtain a recursive expression for the Magnus expansion of the Baker-Campbell-Hausdorff series and an explicit formula in degrees smaller than 5. Our main tool is a non-associative version of the Dynkin-Specht-Wever Lemma. A construction of Bernouilli numbers in terms of binary trees is also recovered. © 2017 American Mathematical Society.