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In the non-commutative version, the role of V is played by the group of characters on a graded connected Hopf algebra, and the role of T by a canonical automorphism associated to the grading. These notions will be defined and illustrated with several examples. The factorization corresponding to the Hopf algebra of quasi-symmetric functions will be one of the main focuses. It involves interesting combinatorial constructions and allows for various applications. |

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