Related papers: Hopf dreams and diagonal harmonics
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general…
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We…
We construct the analogue of Takeuchi's free Hopf algebra in the setting of Poisson Hopf algebras. More precisely, we prove that there exists a free Poisson Hopf algebra on any coalgebra or, equivalently that the forgetful functor from the…
We introduce a new filtration on Hopf algebras, the standard filtration, generalizing the coradical filtration. Its zeroth term, called the Hopf coradical, is the subalgebra generated by the coradical. We give a structure theorem: any Hopf…
We define and study a combinatorial Hopf algebra dRec with basis elements indexed by diagonal rectangulations of a square. This Hopf algebra provides an intrinsic combinatorial realization of the Hopf algebra tBax of twisted Baxter…
We give a new construction of a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (i.e. Baxter permutations, pairs of twin binary trees,…
In this paper, we construct a bialgebraic and further a Hopf algebraic structure on top of subgraphs of a given graph. Further, we give the dual structure of this Hopf algebraic structure. We study the algebra morphisms induced by graph…
Recently, S. Meljanac proposed a construction of a class of examples of an algebraic structure with properties very close to the Hopf algebroids $H$ over a noncommutative base $A$ of other authors. His examples come along with a subalgebra…
We determine the structure of Hopf algebra extensions of a group algebra by the cyclic group of order 2. We study the corepresentation theory of such Hopf algebras, which provide a generalization, at the Hopf algebra level, of the so called…
We construct a new bigraded Hopf algebra whose bases are indexed by square matrices with entries in the alphabet $\{0, 1, ..., k\}$, $k \geq 1$, without null rows or columns. This Hopf algebra generalizes the one of permutations of…
We consider the Hopf algebra of B-diagrams as an algebra projecting onto the Heisenberg algebra and designed to encode the combinatorics of the bosonic normal-ordering problem. In order to understand and generalize the properties of the…
We equip the graded polynomial algebra generated by nonplanar rooted binary trees with a Hopf algebra structure by defining a coproduct which disallows cutting both children of any given vertex, refining Connes-Kreimer's notion of…
In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the Fa\`a di Bruno Hopf algebra, the…
In this article we discuss the Hopf algebras spanned by the adjacency matrices in detail. We show that there two Hopf algebraic structures concerning the adjacency matrices, one is the copy of Connes-Kreimer Hopf algebra, another one is the…
In this article, we are interested in the Hopf algebra $\mathcal{H}_{D}$ of dissection diagrams introduced by Dupont in his thesis. We use the version with a parameter $x\in\mathbb{K}$. We want to study its underlying coalgebra. We…
This paper is an initial inquiry into the structure of the Hopf algebra of matroids with restriction-contraction coproduct. Using a family of matroids introduced by Crapo in 1965, we show that the subalgebra generated by a single point and…
We consider a model for topological recursion based on the Hopf Algebra of planar binary trees of Loday and Ronco. We show that extending this Hopf Algebra by identifying pairs of nearest neighbor leaves and producing in this way graphs…
We investigate several Hopf algebras of diagrams related to Quantum Field Theory of Partitions and whose product comes from the Hopf algebras WSym or WQSym respectively built on integer set partitions and set compositions. Bases of these…
This paper generalizes the operadic construction of the Connes-Kreimer Hopf algebra of rooted trees by Moerdijk. Examples of Hopf algebras obtained in this way include the Loday-Ronco Hopf algebra of planar binary trees and the…
It is well-known that any weak Hopf algebra gives rise to a Hopf algebroid. Moreover it is possible to characterize those Hopf algebroids that arise in this way. Recently, the notion of a weak Hopf algebra has been extended to the case of…