Open AccessPolynomial realizations of some combinatorial Hopf algebras
Author(s) -
Loïc Foissy,
Jean-Christophe Novelli,
JeanYves Thibon
Publication year - 2014
Publication title -
journal of noncommutative geometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.037
H-Index - 26
eISSN - 1661-6960
pISSN - 1661-6952
DOI - 10.4171/jncg/151
Subject(s) - hopf algebra , mathematics , representation theory of hopf algebras , noncommutative geometry , division algebra , quotient , algebra over a field , quantum group , polynomial , quasitriangular hopf algebra , construct (python library) , pure mathematics , algebra representation , combinatorics , discrete mathematics , mathematical analysis , computer science , programming language
20 pagesInternational audienceWe construct explicit polynomial realizations of some combinatorial Hopf algebras based on various kind of trees or forests, and some more general classes of graphs, ranging from the Connes-Kreimer algebra to an algebra of labelled forests isomorphic to the Hopf algebra of parking functions, and to a new noncommutative algebra based on endofunctions admitting many interesting subalgebras and quotients
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