A NON-ASSOCIATIVE BAKER-CAMPBELL-HAUSDORFF FORMULA

Autor(es)

Mostovoy, J. ^[1] ; Perez-Izquierdo, J. M. ^[2] ; Shestakov, I. P. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 145, n. 12, p. 5109-5122, DEC 2017.
• Citações Web of Science: 3

Resumo

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)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático