Natural endomorphisms of quasi-shuffle Hopf algebras
The Hopf algebra of word-quasi-symmetric functions (), a noncommutative generalization of the Hopf algebra of quasi-symmetric functions, can be endowed with an internal product that has several compatibility properties with the other operations on . This extends constructions familiar and central in the theory of free Lie algebras, noncommutative symmetric functions and their various applications fields, and allows to interpret as a convolution algebra of linear endomorphisms of quasi-shuffle...