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April-01-10
8:37 AM
Title: Twisted dendriform algebras and the pre-Lie Magnus expansion
Authors: Kurusch Ebrahimi-Fard, Dominique Manchon
Categories: math.CO Combinatorics (math.QA Quantum Algebra)
Comments: improved version
MSC: 16W30; 05C05; 16W25; 17D25; 37C10; 81T15.
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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