Post-Lie algebras in Regularity Structures
Yvain Bruned, Foivos Katsetsiadis
Abstract
Abstract In this work, we construct the deformed Butcher-Connes-Kreimer Hopf algebra coming from the theory of Regularity Structures as the universal envelope of a post-Lie algebra. We show that this can be done using either of the two combinatorial structures that have been proposed in the context of singular SPDEs: decorated trees and multi-indices. Our construction is inspired from multi-indices where the Hopf algebra was obtained as the universal envelope of a Lie algebra, and it has been proved that one can find a basis that is symmetric with respect to certain elements. We show that this Lie algebra comes from an underlying post-Lie structure.
Topics & Concepts
MathematicsHopf algebraUniversal enveloping algebraAlgebra over a fieldLie algebraGraded Lie algebraLie conformal algebraPure mathematicsAffine Lie algebraLie superalgebraContext (archaeology)Current algebraPaleontologyBiologyAdvanced Topics in AlgebraAlgebraic structures and combinatorial modelsAdvanced Operator Algebra Research