Lie algebras associated to systems of Dyson–Schwinger equations |
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Authors: | Loïc Foissy |
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Institution: | Laboratoire de Mathématiques, Université de Reims, Moulin de la Housse, BP 1039, 51687 Reims Cedex 2, France |
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Abstract: | We consider systems of combinatorial Dyson–Schwinger equations in the Connes–Kreimer Hopf algebra HI of rooted trees decorated by a set I. Let H(S) be the subalgebra of HI generated by the homogeneous components of the unique solution of this system. If it is a Hopf subalgebra, we describe it as the dual of the enveloping algebra of a Lie algebra g(S) of one of the following types:1. g(S) is an associative algebra of paths associated to a certain oriented graph. | 2. Or g(S) is an iterated extension of the Faà di Bruno Lie algebra. | 3. Or g(S) is an iterated extension of an infinite-dimensional abelian Lie algebra. | We also describe the character groups of H(S). |
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Keywords: | MSC: primary 16W30 secondary 81T15 81T18 |
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