Twisted dendriform algebras and the pre-Lie Magnus expansion

TL;DR

This paper introduces twisted dendriform algebras as a framework for Jackson's q-analogues and demonstrates how the pre-Lie Magnus expansion can solve linear q-differential equations.

Contribution

It presents the novel concept of twisted dendriform algebras and applies the pre-Lie Magnus expansion to q-calculus, advancing the algebraic tools for q-differential equations.

Findings

Application of pre-Lie Magnus expansion to Jackson's q-integral

Introduction of twisted dendriform algebras for q-analogues

Solution method for linear q-differential equations

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.