Crossed morphisms, integration of post-Lie algebras and the post-Lie Magnus expansion

Autor(es)

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

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Sao Carlos, SP - Brazil

^[2] Univ Malaga, Dept Algebra Geometria & Topol, Malaga - Spain

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN ALGEBRA; v. 49, n. 8, p. 3507-3533, JUL 7 2021.
• Citações Web of Science: 0

Resumo

This letter is divided in two parts. In the first one it will be shown that the datum of a post-Lie product is equivalent to the one of an invertible crossed morphism between two Lie algebras. Moreover it will be argued that the integration of such a crossed morphism yields the post-Lie Magnus expansion associated to the original post-Lie algebra. The second part is devoted to present two combinatorial methods to compute the coefficients of this remarkable formal series. Both methods are based on special tubings on planar trees. (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