Post-symmetric braces and integration of post-Lie algebras

Author(s)

Mencattini, Igor ^[1] ; Quesney, Alexandre ^[1] ; Silva, Pryscilla ^[2]

Affiliation

^[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

• Document type: Journal article
• Source: Journal of Algebra; v. 556, p. 547-580, AUG 15 2020.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 18/19603-0 - Homotopy and root theory, manifold theory, stratified spaces, spherical space forms and topological dynamic systems.
• Grantee: Alexandre Thomas Guillaume Quesney
• Support Opportunities: Scholarships in Brazil - Post-Doctoral