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Natural endomorphisms of quasi-shuffle Hopf algebras

Jean-Christophe Novelli, Frédéric Patras, Jean-Yves Thibon (2013)

Bulletin de la Société Mathématique de France

The Hopf algebra of word-quasi-symmetric functions ( 𝐖𝐐𝐒𝐲𝐦 ), 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 𝐖𝐐𝐒𝐲𝐦 . 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 𝐖𝐐𝐒𝐲𝐦 as a convolution algebra of linear endomorphisms of quasi-shuffle...

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