Post-Lie algebras and factorization theorems

Abstract

In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions) of those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.

References in corpus (3)

• Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion
• A Magnus- and Fer-type formula in dendriform algebras
• Post-Lie Algebras and Isospectral Flows

Cited by in corpus (10)

• What is a post-Lie algebra and why is it useful in geometric integration
• Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation
• The Magnus expansion and Post-Lie algebras
• $3$-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras
• What is the Magnus Expansion?
• Post-Lie Algebras, Factorization Theorems and Isospectral-Flows
• Combinatorial Hopf algebra for interconnected nonlinear systems
• Post-Lie algebra structures on the Witt algebra
• Formal integration of complete Rota-Baxter Lie algebras
• On the sub-adjacent Hopf algebra of the universal enveloping algebra of a post-Lie algebra