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We analyze the structure of theMalvenuto-Reutenauer Hopf algebraSSym of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primiti...
Loday and Ronco defined an interesting Hopf algebra structure on the linear span of the set of planar binary trees. They showed that the inclusion of the Hopf algebra of non-commutative symmetric fu...
We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results are closely related to the fact that uniform block permutations form a fact...
We study P-Hopf algebras with one coassociative cooperation over different operads P. For example, we consider the Loday-Ronco dendriform Hopf algebra and its isomorphisms with the noncommutative plan...
Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to ...
Abstract: We consider a q-analogue of the standard bilinear form on the commutative ring of symmetric functions. The q=-1 case leads to a Z-graded Hopf superalgebra which we call the algebra of odd sy...
Noncommutative oscillators are first-quantized through an abelian Drinfel’d twist deformation of a Hopf algebra and its action on a module. Several impor-tant and subtle issues making possible the qua...
The graph algebra is a commutative, cocommutative, graded,connected incidence Hopf algebra, whose basis elements correspond to fi-nite simple graphs and whose Hopf product and coproduct admit simple c...
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 Hop...
We define a super version of the Connes-Moscovici Hopf algebra, $\mathcal{H}_1$. For that, we consider the supergroup $G^s=Diff^+(\mathbb{R}^{1,1})$ of orientation preserving diffeomorphisms of the s...
The relation between Connes-Kreimer Hopf algebra approach to renormalization and deformation quantization is investigated. Both approaches rely on factorization, the correspondence being established...
The renormalization of quantum field theory twists the antipode of a noncocommutative Hopf algebra of rooted trees, decorated by an infinite set of primitive divergences. The Hopf algebra of undecorat...

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