Post-Lie Algebras and Isospectral Flows
Kurusch Ebrahimi-Fard, Alexander Lundervold, Igor Mencattini, Hans Z., Munthe-Kaas
TL;DR
This paper investigates the structure of post-Lie algebras derived from classical R-matrices, providing explicit solutions for associated Lie bracket flows using a post-Lie Magnus-type differential equation.
Contribution
It introduces a novel approach to solving Lie bracket flows in post-Lie algebras via a Magnus-type differential equation, expanding understanding of their algebraic and dynamic properties.
Findings
Explicit exponential solutions for Lie bracket flows
Development of a post-Lie Magnus-type differential equation
Enhanced understanding of Lie enveloping algebras from post-Lie structures
Abstract
In this paper we explore the Lie enveloping algebra of a post-Lie algebra derived from a classical -matrix. An explicit exponential solution of the corresponding Lie bracket flow is presented. It is based on the solution of a post-Lie Magnus-type differential equation.
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