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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A NON-ASSOCIATIVE BAKER-CAMPBELL-HAUSDORFF FORMULA

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Author(s):
Mostovoy, J. [1] ; Perez-Izquierdo, J. M. [2] ; Shestakov, I. P. [3]
Total Authors: 3
Affiliation:
[1] IPN, Dept Matemat, CINVESTAV, Apartado Postal 14-740, Mexico City 07000, DF - Mexico
[2] Univ La Rioja, Dept Matemat & Computac, Logrono 26004 - Spain
[3] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05311970 Sao Paulo, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: Proceedings of the American Mathematical Society; v. 145, n. 12, p. 5109-5122, DEC 2017.
Web of Science Citations: 3
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. (AU)

FAPESP's process: 14/09310-5 - Algebraic structures and their representations
Grantee:Vyacheslav Futorny
Support Opportunities: Research Projects - Thematic Grants