Twisted dendriform algebras and the pre-Lie Magnus expansion |
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Authors: | Kurusch Ebrahimi-Fard Dominique Manchon |
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Institution: | a Department de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, E-50009 Zaragoza, Spainb Université Blaise Pascal, C.N.R.S.-UMR 6620 63177 Aubière, France |
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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-analogs, 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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Keywords: | Primary 16W30 05C05 16W25 17D25 37C10 Secondary 81T15 |
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