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Tridendriform structure on combinatorial Hopf algebras by Emily Burgunder; María Ronco is a Mathematics article available to read on EtoBox.

What is Tridendriform structure on combinatorial Hopf algebras about?

We extend the definition of tridendriform bialgebra by introducing a parameter q. The subspace of primitive elements of a qtridendriform bialgebra is equipped with an associative product and a natural structure of brace algebra, related by a distributive law. This data is called q-Gerstenhaber-Voronov algebras. We prove the equivalence between the categories of conilpotent qtridendriform bialgebras and of q-Gerstenhaber-Voronov algebras. The space spanned by surjective maps between finite sets, as well as the space spanned by parking functions, have a natural structure of q-tridendriform bialgebra, denoted ST(q) and PQSym(q) \* , in such a way that ST(q) is a sub-tridendriform bialgebra of PQSym(q) \* . Finally we show that the bialgebra of M-permutations defined by T. Lam and P. Pylyavskyy comes from a q-tridendriform algebra which is a quotient of ST(q).

Who reads Tridendriform structure on combinatorial Hopf algebras?

Author

Emily Burgunder; María Ronco

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0021-8693)

Published

2010

Language

EN

Field

Mathematics (Physical Sciences)