scholarly journals Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras

2016 ◽  
Vol Vol. 17 no. 3 (Combinatorics) ◽  
Author(s):  
Nguyen Hoang-Nghia ◽  
Adrian Tanasa ◽  
Christophe Tollu
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Algebra Structure ◽  
Isomorphism Classes ◽  
Hopf Algebra Structure ◽  
International Audience

International audience We endow the set of isomorphism classes of matroids with a new Hopf algebra structure, in which the coproduct is implemented via the combinatorial operations of restriction and deletion. We also initiate the investigation of dendriform coalgebra structures on matroids and introduce a monomial invariant which satisfy a convolution identity with respect to restriction and deletion.

HOPF-ALGEBRAIC ASPECTS OF ITERATED STOCHASTIC INTEGRALS

2009 ◽  
Vol 12 (03) ◽  
pp. 479-496 ◽  
Author(s):  
R. L. HUDSON
Keyword(s):  
Hopf Algebra ◽  
Explicit Formula ◽  
Hopf Algebras ◽  
Stochastic Integrals ◽  
Algebra Structure ◽  
Hopf Algebra Structure

An explicit formula is found for the antipode in Itô–Hopf algebras. The Hopf algebra structure is extended to iterated classical and quantum stochastic integrals. The antipode is related to change of orientation in the simplicial domains of such integrals.

scholarly journals Combinatorial Hopf algebra of supercharacters of type D

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Carolina Benedetti
Keyword(s):  
Hopf Algebra ◽  
Finite Field ◽  
Type A ◽  
The Other ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Type D ◽  
International Audience ◽  
Supercharacter Theory ◽  
Triangular Group

International audience We provide a Hopf algebra structure on the supercharacter theory for the unipotent upper triangular group of type {D} over a finite field. Also, we make further comments with respect to types {B} and {C}. Type {A} was explored by M. Aguiar et. al (2010), thus this extended abstract is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types. Dotamos con una estructura de álgebra de Hopf la teoría de supercaracteres del grupo de matrices unipotentes triangulares superiores de tipo{D} sobre un cuerpo finito. Ademas, discutimos brevemente los tipos {B} y {C}. El tipo A fue explorado por M. Aguiar et al (2010), por lo tanto este resumen extendido es una contribución para entender combinatoriamente la teoría de supercaracteres de los otros tipos de Lie clásicos. Nous construisons une structure d'algèbre de Hopf sur la thérie des supercharactères du groupe de matrices unipotentes triangulaires supéieures de type {D}. Nous donnons aussi quelques commentaires à l'égard des types {B} et {C} . Le type {A} a été explorée par M. Aguiar et al. (2010), donc ce résumé étendu est une contribution à la théorie combinatoire des supercharactères pour les autres types de Lie classiques. \par

scholarly journals Hopf Algebra Structure of Generalized Quasi-Symmetric Functions in Partially Commutative Variables

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Adam Doliwa
Keyword(s):  
Power Series ◽  
Hopf Algebra ◽  
Hopf Algebras ◽  
Symmetric Functions ◽  
Algebra Structure ◽  
Natural Basis ◽  
Dual Algebra ◽  
Power Sum ◽  
Hopf Algebra Structure

We introduce a coloured generalization  $\mathrm{NSym}_A$ of the Hopf algebra of non-commutative symmetric functions  described as a subalgebra of the of rooted ordered coloured trees Hopf algebra. Its natural basis can be identified with the set of sentences over alphabet $A$ (the set of colours). We present also its graded dual algebra $\mathrm{QSym}_A$ of coloured quasi-symmetric functions together with its realization in terms of power series in partially commutative variables.  We provide formulas expressing multiplication, comultiplication and the antipode for these Hopf algebras in various bases — the corresponding generalizations of the complete homogeneous, elementary, ribbon Schur and power sum bases of $\mathrm{NSym}$, and the monomial and fundamental bases of $\mathrm{QSym}$. We study also certain distinguished series of trees in the setting of restricted duals to Hopf algebras.

scholarly journals A Hopf algebra of subword complexes (Extended abstract)

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Nantel Bergeron ◽  
Cesar Ceballos
Keyword(s):  
Hopf Algebra ◽  
Cluster Algebras ◽  
Algebra Structure ◽  
Acyclic Orientations ◽  
Hopf Algebra Structure ◽  
International Audience

International audience We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf algebra induces a natural non-trivial sub-Hopf algebra on c-clusters in the theory of cluster algebras.

scholarly journals Hopf algebra structure of Grq(1|1) related to GLq(1|1)

1999 ◽  
Vol 40 (5) ◽  
pp. 2494-2499 ◽  
Author(s):  
Salih Çelik
Keyword(s):  
Hopf Algebra ◽  
Algebra Structure ◽  
Hopf Algebra Structure

Some Results in the Connective K-Theory of Lie Groups

1988 ◽  
Vol 31 (2) ◽  
pp. 194-199
Author(s):  
L. Magalhães
Keyword(s):  
Hopf Algebra ◽  
Lie Groups ◽  
Lie Group ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
K Theory ◽  
Torsion Free ◽  
Connected Lie Group

AbstractIn this paper we give a description of:(1) the Hopf algebra structure of k*(G; L) when G is a compact, connected Lie group and L is a ring of type Q(P) so that H*(G; L) is torsion free;(2) the algebra structure of k*(G2; L) for L = Z2 or Z.

scholarly journals Hopf algebra structure of symmetric and quasisymmetric functions in superspace

2019 ◽  
Vol 166 ◽  
pp. 144-170
Author(s):  
Susanna Fishel ◽  
Luc Lapointe ◽  
María Elena Pinto
Keyword(s):  
Hopf Algebra ◽  
Algebra Structure ◽  
Quasisymmetric Functions ◽  
Hopf Algebra Structure
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