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 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 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 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

scholarly journals ON THE COALGEBRAIC RING AND BOUSFIELD–KAN SPECTRAL SEQUENCE FOR A LANDWEBER EXACT SPECTRUM

2004 ◽  
Vol 47 (3) ◽  
pp. 513-532 ◽  
Author(s):  
Martin Bendersky ◽  
John R. Hunton
Keyword(s):  
Hopf Algebra ◽  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
Subject Classification ◽  
Homotopy Groups ◽  
Algebra Structure ◽  
Simple Description ◽  
Ring Spectrum ◽  
Hopf Algebra Structure

AbstractWe construct a Bousfield–Kan (unstable Adams) spectral sequence based on an arbitrary (and not necessarily connective) ring spectrum $E$ with unit and which is related to the homotopy groups of a certain unstable $E$ completion $X_E^{\wedge}$ of a space $X$. For $E$ an $\mathbb{S}$-algebra this completion agrees with that of the first author and Thompson. We also establish in detail the Hopf algebra structure of the unstable cooperations (the coalgebraic module) $E_*(\underline{E}_*)$ for an arbitrary Landweber exact spectrum $E$, extending work of the second author with Hopkins and with Turner and giving basis-free descriptions of the modules of primitives and indecomposables. Taken together, these results enable us to give a simple description of the $E_2$-page of the $E$-theory Bousfield–Kan spectral sequence when $E$ is any Landweber exact ring spectrum with unit. This extends work of the first author and others and gives a tractable unstable Adams spectral sequence based on a $v_n$-periodic theory for all $n$.AMS 2000 Mathematics subject classification: Primary 55P60; 55Q51; 55S25; 55T15. Secondary 55P47

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