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Journal articles on the topic 'Algèbres de Hopf bidendriformes'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

Loday, Jean-Louis, and Marı́a Ronco. "Algèbres de Hopf colibres." Comptes Rendus Mathematique 337, no. 3 (2003): 153–58. http://dx.doi.org/10.1016/s1631-073x(03)00288-7.

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2

Vallin, Jean-Michel. "C* -Algèbres de Hopf et C* -Algèbres de Kac." Proceedings of the London Mathematical Society s3-50, no. 1 (1985): 131–74. http://dx.doi.org/10.1112/plms/s3-50.1.131.

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3

Novelli, Jean-Christophe, Jean-Yves Thibon, and Nicolas M. Thiéry. "Algèbres de Hopf de graphes." Comptes Rendus Mathematique 339, no. 9 (2004): 607–10. http://dx.doi.org/10.1016/j.crma.2004.09.012.

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4

Bichon, Julien. "N-complexes et algèbres de Hopf." Comptes Rendus Mathematique 337, no. 7 (2003): 441–44. http://dx.doi.org/10.1016/j.crma.2003.09.002.

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5

Chapoton, Frédéric. "Algèbres pré-Lie et algèbres de Hopf liées à la renormalisation." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 332, no. 8 (2001): 681–84. http://dx.doi.org/10.1016/s0764-4442(01)01919-x.

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6

Blanchard, Etienne. "Déformations de $C\sp*$-algèbres de Hopf." Bulletin de la Société mathématique de France 124, no. 1 (1996): 141–215. http://dx.doi.org/10.24033/bsmf.2278.

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7

Patras, Frédéric. "La décomposition en poids des algèbres de Hopf." Annales de l’institut Fourier 43, no. 4 (1993): 1067–87. http://dx.doi.org/10.5802/aif.1365.

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8

Chapoton, Frédéric. "Algèbres de Hopf des permutahèdres, associahèdres et hypercubes." Advances in Mathematics 150, no. 2 (2000): 264–75. http://dx.doi.org/10.1006/aima.1999.1868.

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9

Foissy, L. "Les algèbres de Hopf des arbres enracinés décorés, I." Bulletin des Sciences Mathématiques 126, no. 3 (2002): 193–239. http://dx.doi.org/10.1016/s0007-4497(02)01108-9.

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10

Foissy, L. "Les algèbres de Hopf des arbres enracinés décorés, II." Bulletin des Sciences Mathématiques 126, no. 4 (2002): 249–88. http://dx.doi.org/10.1016/s0007-4497(02)01113-2.

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11

Baaj, Saad, and Georges Skandalis. "C*-algèbres de Hopf et théorie de Kasparov équivariante." K-Theory 2, no. 6 (1989): 683–721. http://dx.doi.org/10.1007/bf00538428.

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12

Belhaj Mohamed, Mohamed. "Groupes de renormalisation pour deux algèbres de Hopf en produit semi-direct." Annales de la faculté des sciences de Toulouse Mathématiques 22, no. 2 (2013): 421–44. http://dx.doi.org/10.5802/afst.1377.

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13

BONNEAU, PHILIPPE. "TOPOLOGICAL QUANTUM DOUBLE." Reviews in Mathematical Physics 06, no. 02 (1994): 305–18. http://dx.doi.org/10.1142/s0129055x94000146.

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Following a preceding paper showing how the introduction of a t.v.s. topology on quantum groups led to a remarkable unification and rigidification of the different definitions, we adapt here, in the same way, the definition of quantum double. This topological double is dualizable and reflexive (even for infinite dimensional algebras). In a simple case we show, considering the double as the "zero class" of an extension theory, the uniqueness of the double structure as a quasi-Hopf algebra. A la suite d'un précédent article montrant comment l'introduction d'une topologie d'e.v.t. sur les groupes

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14

Foissy, L. "Quantifications des algèbres de Hopf d'arbres plans décorés et lien avec les groupes quantiques." Bulletin des Sciences Mathématiques 127, no. 6 (2003): 505–48. http://dx.doi.org/10.1016/s0007-4497(03)00028-9.

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15

Bergeron, Nantel, Thomas Lam, and Huilan Li. "Combinatorial Hopf Algebras and Towers of Algebras." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AJ,..., Proceedings (2008). http://dx.doi.org/10.46298/dmtcs.3634.

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International audience Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n \geq 0}A_n$ can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of algebras. We show that if a tower $\bigoplus_{n \geq 0}A_n$ gives rise to graded dual Hopf algebras then we must have $\dim (A_n)=r^nn!$ where $r = \dim (A_1)$. Berg

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16

Law, Shirley. "Hopf Algebra of Sashes." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AT,..., Proceedings (2014). http://dx.doi.org/10.46298/dmtcs.2428.

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International audience A general lattice theoretic construction of Reading constructs Hopf subalgebras of the Malvenuto-Reutenauer Hopf algebra (MR) of permutations. The products and coproducts of these Hopf subalgebras are defined extrinsically in terms of the embedding in MR. The goal of this paper is to find an intrinsic combinatorial description of a particular one of these Hopf subalgebras. This Hopf algebra has a natural basis given by permutations that we call Pell permutations. The Pell permutations are in bijection with combinatorial objects that we call sashes, that is, tilings of a

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17

Aguiar, Marcelo, Carlos André, Carolina Benedetti, et al. "Supercharacters, symmetric functions in noncommuting variables (extended abstract)." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AO,..., Proceedings (2011). http://dx.doi.org/10.46298/dmtcs.2967.

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International audience We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras. Nous montrons que deux structures en apparence bien différentes peuvent être identifiées: les super-car

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18

Bultel, Jean-Paul, Ali Chouria, Jean-Gabriel Luque, and Olivier Mallet. "Redfield-Pólya theorem in $\mathrm{WSym}$." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AS,..., Proceedings (2013). http://dx.doi.org/10.46298/dmtcs.2324.

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International audience We give noncommutative versions of the Redfield-Pólya theorem in $\mathrm{WSym}$, the algebra of word symmetric functions, and in other related combinatorial Hopf algebras. Nous donnons des versions non-commutatives du théorème d’énumération de Redfield-Pólya dans $\mathrm{WSym}$, l’algèbre des fonctions symétriques sur les mots, ainsi que dans d’autres algèbres de Hopf combinatoires.

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19

Aval, Jean-Christophe, Jean-Christophe Novelli, and Jean-Yves Thibon. "The # product in combinatorial Hopf algebras." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AO,..., Proceedings (2011). http://dx.doi.org/10.46298/dmtcs.2892.

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International audience We show that the # product of binary trees introduced by Aval and Viennot (2008) is in fact defined at the level of the free associative algebra, and can be extended to most of the classical combinatorial Hopf algebras. Nous montrons que le produit # introduit par Aval et Viennot (2008) est défini au niveau de l'algèbre associative libre, et peut être étendu à la plupart des algèbres de Hopf combinatoires classiques.

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20

Priez, Jean-Baptiste. "Lattice of combinatorial Hopf algebras: binary trees with multiplicities." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AS,..., Proceedings (2013). http://dx.doi.org/10.46298/dmtcs.2372.

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International audience In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras. As an application, we construct a new combinatorial Hopf algebra on binary trees with multiplicities and use it to prove a hook length formula for those trees. Dans une première partie, nous formalisons la construction d’algèbres de Hopf combinatoires à partir d’une réalisation polynomiale et de monoïdes de type monoïde plaxique. Grâce à cette c

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21

Benedetti, Carolina, Joshua Hallam, and John Machacek. "Combinatorial Hopf Algebras of Simplicial Complexes." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 27th..., Proceedings (2015). http://dx.doi.org/10.46298/dmtcs.2506.

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International audience We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra. The characters of these Hopf algebras give rise to symmetric functions that encode information about colorings of simplicial complexes and their $f$-vectors. We also use characters to give a generalization of Stanley’s $(-1)$-color theorem. Nous considérons une algèbre de Hopf de complexes simpliciaux et fournissons une formule sans multiplicité pour son

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22

Pang, C. Y. Amy. "Card-Shuffling via Convolutions of Projections on Combinatorial Hopf Algebras." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 27th..., Proceedings (2015). http://dx.doi.org/10.46298/dmtcs.2511.

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International audience Recently, Diaconis, Ram and I created Markov chains out of the coproduct-then-product operator on combinatorial Hopf algebras. These chains model the breaking and recombining of combinatorial objects. Our motivating example was the riffle-shuffling of a deck of cards, for which this Hopf algebra connection allowed explicit computation of all the eigenfunctions. The present note replaces in this construction the coproduct-then-product map with convolutions of projections to the graded subspaces, effectively allowing us to dictate the distribution of sizes of the pieces in

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23

Lam, Thomas, Aaron Lauve, and Frank Sottile. "Skew Littlewood―Richardson rules from Hopf algebras." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AN,..., Proceedings (2010). http://dx.doi.org/10.46298/dmtcs.2853.

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International audience We use Hopf algebras to prove a version of the Littlewood―Richardson rule for skew Schur functions, which implies a conjecture of Assaf and McNamara. We also establish skew Littlewood―Richardson rules for Schur $P-$ and $Q-$functions and noncommutative ribbon Schur functions, as well as skew Pieri rules for k-Schur functions, dual k-Schur functions, and for the homology of the affine Grassmannian of the symplectic group. Nous utilisons des algèbres de Hopf pour prouver une version de la règle de Littlewood―Richardson pour les fonctions de Schur gauches, qui implique une

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24

Aguiar, Marcelo, and Aaron Lauve. "Convolution Powers of the Identity." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AS,..., Proceedings (2013). http://dx.doi.org/10.46298/dmtcs.2365.

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International audience We study convolution powers $\mathtt{id}^{\ast n}$ of the identity of graded connected Hopf algebras $H$. (The antipode corresponds to $n=-1$.) The chief result is a complete description of the characteristic polynomial - both eigenvalues and multiplicity - for the action of the operator $\mathtt{id}^{\ast n}$ on each homogeneous component $H_m$. The multiplicities are independent of $n$. This follows from considering the action of the (higher) Eulerian idempotents on a certain Lie algebra $\mathfrak{g}$ associated to $H$. In case $H$ is cofree, we give an alternative (e

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25

Forcey, Stefan, Aaron Lauve, and Frank Sottile. "New Hopf Structures on Binary Trees." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AK,..., Proceedings (2009). http://dx.doi.org/10.46298/dmtcs.2740.

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International audience The multiplihedra $\mathcal{M}_{\bullet} = (\mathcal{M}_n)_{n \geq 1}$ form a family of polytopes originating in the study of higher categories and homotopy theory. While the multiplihedra may be unfamiliar to the algebraic combinatorics community, it is nestled between two families of polytopes that certainly are not: the permutahedra $\mathfrak{S}_{\bullet}$ and associahedra $\mathcal{Y}_{\bullet}$. The maps $\mathfrak{S}_{\bullet} \twoheadrightarrow \mathcal{M}_{\bullet} \twoheadrightarrow \mathcal{Y}_{\bullet}$ reveal several new Hopf structures on tree-like objects

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