Post-symmetric braces and integration of post-Lie algebras

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Autor(es):	Mencattini, Igor ^[1] ; Quesney, Alexandre ^[1] ; Silva, Pryscilla ^[2] Número total de Autores: 3
Afiliação do(s) autor(es):	^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400, Sao Carlos 13566590, SP - Brazil ^[2] Univ Estadual Santa Cruz, Dept Ciencias Exatas, Campus Soane Nazare Andrade, Rodovia Jorge Amado, Ilheus 45662900, BA - Brazil Número total de Afiliações: 2
Tipo de documento:	Artigo Científico
Fonte:	Journal of Algebra; v. 556, p. 547-580, AUG 15 2020.
Citações Web of Science:	0
Resumo
The aim of this letter is twofold. Firstly, we introduce the post-Lie analogue of the notion of a symmetric brace algebra, termed in the sequel post-symmetric brace algebra. These brace algebras are defined using a suitable algebraic operad, which turns out to be isomorphic to the operad, of the post-Lie algebras. Secondly, using these new brace algebras, together with the so called post-Lie Magnus expansion, we aim both to analyze the enveloping algebra of the corresponding post-Lie algebra and to compare the two Baker-Campbell-Hausdorff series there naturally defined. (C) 2020 Elsevier Inc. All rights reserved. (AU)

Processo FAPESP:	18/19603-0 - Teoria de Homotopia e de Raizes, Topologia de Variedades, Espaços Estratificados, Formas Espaciais Esféricas e Sistemas Dinâmicos Topológicos.
Beneficiário:	Alexandre Thomas Guillaume Quesney
Modalidade de apoio:	Bolsas no Brasil - Pós-Doutorado