Twisted dendriform algebras and the pre-Lie Magnus expansion
نویسندگان
چکیده
منابع مشابه
Infinitesimal Bialgebras, Pre-lie and Dendriform Algebras
We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesimal version of the double. We show that there is a natural, but non-obvious way to construct a pre-Lie algebra from an arbitrary infinitesimal bialgebra and a dendriform algebra from a quasitriangular infinitesimal bial...
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We provide a refined approach to the classical Magnus [Mag54] and Fer expansion [F58], unveiling a new structure by using the language of dendriform and pre-Lie algebras. The recursive formula for the logarithm of the solutions of the equations X = 1 + λa ≺ X and Y = 1− λY ≻ a in A[[λ]] is provided, where (A,≺,≻) is a dendriform algebra. Then, we present the solutions to these equations as an i...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2011
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2011.03.004