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Lie-Butcher series, Geometry, Algebra and Computation | | Hans Z. Munthe-Kaas
; Kristoffer K. Føllesdal
; | | Date: |
13 Jan 2017 | | Abstract: | Lie-Butcher (LB) series are formal power series expressed in terms of trees
and forests. On the geometric side LB-series generalizes classical B-series
from Euclidean spaces to Lie groups and homogeneous manifolds. On the algebraic
side, B-series are based on pre-Lie algebras and the Butcher-Connes-Kreimer
Hopf algebra. The LB-series are instead based on post-Lie algebras and their
enveloping algebras. Over the last decade the algebraic theory of LB-series has
matured. The purpose of this paper is twofold. First, we aim at presenting the
algebraic structures underlying LB series in a concise and self contained
manner. Secondly, we review a number of algebraic operations on LB-series found
in the literature, and reformulate these as recursive formulae. This is part of
an ongoing effort to create an extensive software library for computations in
LB-series and B-series in the programming language Haskell. | | Source: | arXiv, 1701.3654 | | Services: | Forum | Review | PDF | Favorites | |
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