Twisted dendriform algebras and the pre-Lie Magnus expansion Article - Novembre 2011

Kurusch Ebrahimi-Fard, Dominique Manchon

Kurusch Ebrahimi-Fard, Dominique Manchon, « Twisted dendriform algebras and the pre-Lie Magnus expansion  », Journal of Pure and Applied Algebra, novembre 2011. ISSN 0022-4049

Abstract

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.

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