Article: On the Lie enveloping algebra of a post-Lie algebra
Authors: Kurusch Ebrahimi-Fard, Alexander Lundervold, Hans Munthe-Kaas
Journal: Journal of Lie Theory, 25(4):1139-1165.
Abstract: We consider pairs of Lie algebras g and ̄g*, defined over a common vector space, where the Lie brackets of g and ̄g* are related via a post- Lie algebra structure. The latter can be extended to the Lie enveloping algebra U(g). This permits us to define another associative product on U(g), which gives rise to a Hopf algebra isomorphism between U(g) and a new Hopf algebra assembled from U(g*) with the new product.
For the free post-Lie algebra these constructions provide a refined understanding of a fundamental Hopf algebra appearing in the theory of numerical integration methods for differential equations on manifolds. In the pre-Lie setting, the algebraic point of view developed here also pro- vides a concise way to develop Butcher’s order theory for Runge–Kutta methods.
Hindsight notes: None yet.
24 Oct 2014