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

ON ALGEBRAIC SUPERGROUPS AND QUANTUM DEFORMATIONS

2003 ◽  
Vol 02 (04) ◽  
pp. 403-423 ◽  
Author(s):  
R. FIORESI
Keyword(s):  
Hopf Algebra ◽  
The Other ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Quantum Deformations ◽  
Functor Of Points ◽  
Algebraic Supergroup

We give the definitions of affine algebraic supervariety and affine algebraic supergroup through the functor of points and we relate them to the other definitions present in the literature. We study in detail the algebraic supergroups GL(m|n) and SL(m|n) and give explicitly the Hopf algebra structure of the algebra representing the functors of points. In the end we also give the quantization of GL(m|n) together with its coaction on suitable quantum spaces according to Manin's philosophy.

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.

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 Crossings and nestings in set partitions of classical types

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Martin Rubey ◽  
Christian Stump
Keyword(s):  
Nous Avons ◽  
Type A ◽  
The Other ◽  
Type B ◽  
Set Partition ◽  
Set Partitions ◽  
Type D ◽  
Nous Montrons ◽  
International Audience ◽  
The One

International audience In this extended abstract, we investigate bijections on various classes of set partitions of classical types that preserve openers and closers. On the one hand we present bijections for types $B$ and $C$ that interchange crossings and nestings, which generalize a construction by Kasraoui and Zeng for type $A$. On the other hand we generalize a bijection to type $B$ and $C$ that interchanges the cardinality of a maximal crossing with the cardinality of a maximal nesting, as given by Chen, Deng, Du, Stanley and Yan for type $A$. For type $D$, we were only able to construct a bijection between non-crossing and non-nesting set partitions. For all classical types we show that the set of openers and the set of closers determine a non-crossing or non-nesting set partition essentially uniquely. Dans ce résumé, nous étudions des bijections entre diverses classes de partitions d'ensemble de types classiques qui préservent les "openers'' et les "closers''. D'une part, nous présentons des bijections pour les types $B$ et $C$ qui échangent croisées et emboôtées, qui généralisent une construction de Kasraoui et Zeng pour le type $A$. D'autre part, nous généralisons une bijection pour le type $B$ et $C$ qui échange la cardinalité d'un croisement maximal avec la cardinalité d'un emboîtement maximal comme il a été fait par Chen, Deng, Du, Stanley et Yan pour le type $A$. Pour le type $D$, nous avons seulement construit une bijection entre les partitions non croisées et non emboîtées. Pour tout les types classiques, nous montrons que l'ensemble des "openers'' et l'ensemble des "closers'' déterminent une partition non croisées ou non emboîtées essentiellement de façon unique.

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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