Twisted dendriform algebras and the pre-Lie Magnus expansion

Details Twisted dendriform algebras and the pre-Lie Magnus expansion Twisted dendriform algebras and the pre-Lie Magnus expansion

2009-10-12

arxiv.org/abs/0910.2166v3

Journal of Pure and Applied Algebra 215 (2011) 2615-2627

Mathematics

Combinatorics

improved version; accepted for publication in the Journal of Pure & Applied Algebra

Scientific paper

10.1016/j.jpaa.2011.03.004

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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