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.