A rooted-trees<i>q</i>-series lifting a one-parameter family of Lie idempotents

Chapoton, Frédéric

doi:10.2140/ant.2009.3.611

Cited by 32 publications

(45 citation statements)

References 24 publications

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“…This point of view motivated us to explore the solution theory of a particular class of linear dendriform equations [18] appearing in the contexts of different applications, such as for instance perturbative renormalization in quantum field theory. Our results fit into recent developments exploring algebro-combinatorial aspects related to Magnus' work [9,10,19,24]. In both Refs.…”

Section: Introductionsupporting

confidence: 88%

Twisted dendriform algebras and the pre-Lie Magnus expansion

Ebrahimi‐Fard

Manchon

2011

Journal of Pure and Applied Algebra

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In this paper an application of the recently introduced pre-Lie Magnus expansion to Jackson's q-integral and q-exponentials is presented. Twisted dendriform algebras, which are the natural algebraic framework for Jackson's q-analogues, are introduced for that purpose. It is shown how the pre-Lie Magnus expansion is used to solve linear q-differential equations. We also briefly outline the theory of linear equations in twisted dendriform algebras.Comment: improved version; accepted for publication in the Journal of Pure & Applied Algebr

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Section: Introductionsupporting

confidence: 88%

Twisted dendriform algebras and the pre-Lie Magnus expansion

Ebrahimi‐Fard

Manchon

2011

Journal of Pure and Applied Algebra

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“…In the context of combinatorial Hopf algebras the coefficients ω can be traced back to [11] under the name log * and are studied also in [8,12,22,40]. The coefficients ω(τ) may be computed by induction from the relation ω⋆e= δ ∅ + δ using formula (17).…”

Section: Explicit Formula For the Logarithmic Mapmentioning

confidence: 99%

Algebraic Structures of B-series

2010

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B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elegant derivation of order conditions, and a substitution law gives much insight into modified differential equations of backward error analysis. These two laws give rise to algebraic structures (groups and Hopf algebras of trees) that have recently received much attention also in the non-numerical literature. This article emphasizes these algebraic structures and presents interesting relationships among them.

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“…Ces fractions ont été définies par Carlitz [1,2], puis étudiées par Koblitz et Satoh [6,8]. Elles sont aussi apparues plus récemment dans [3], avec une motivation algébrique.…”

Section: Fractions De Bernoulli-carlitzunclassified