A non-associative baker-campbell-hausdorff formula
- Mostovoy, J. 1
- Pérez-Izquierdo, J.M. 2
- Shestakov, I.P. 3
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1
Instituto Politécnico Nacional
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2
Universidad de La Rioja
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3
Universidade de São Paulo
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ISSN: 0002-9939
Year of publication: 2017
Volume: 145
Issue: 12
Pages: 5109-5122
Type: Article
More publications in: Proceedings of the American Mathematical Society
Related Projects
2014/00067/001
Abstract
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.