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1. Algebra and Number Theory

Generalized Faà di Bruno Hopf algebras

Yinhuo Zhang
University of Hasselt, Belgium

Abstract:

We introduce the (m,g,a0)-Bell polynomials to construct the graded pointed Hopf algebras H(m,g)FbB and their Hopf Ore extensions, which contain the well-known Faà di Bruno Hopf algebra. We then give the isomorphism theorem of those Hopf algebras and study their Hopf subalgebras. The noncommutative versions of H(1,gr1)FbB are determined. Finally, we use some special Lyndon words to construct several free bialgebras containing some basic combinatorial bialgebras and the noncommutative Faà di Bruno bialgebra as quotients.