Combinatorial Hopf Algebras and Towers of Algebras

ar X iv : 0 90 3 . 13 81 v 1 [ m at h . C O ] 8 M ar 2 00 9 COMBINATORIAL HOPF ALGEBRAS AND TOWERS OF ALGEBRAS – DIMENSION , QUANTIZATION , AND FUNCTORIALITY

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras L n≥0 An 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 al...

On the partial categorification of some Hopf algebras using the representation theory of towers of J -trivial monoids and semilattices

This paper considers the representation theory of towers of algebras of J -trivial monoids. Using a very general lemma on induction, we derive a combinatorial description of the algebra and coalgebra structure on the Grothendieck rings G0 and K0. We then apply our theory to some examples. We first retrieve the classical Krob-Thibon’s categorification of the pair of Hopf algebras QSym/NCSF as re...

On the Coderivations of Some Hopf Algebras

Gorenstein global dimensions for Hopf algebra actions

Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra‎. ‎In this paper‎, ‎we investigate Gorenstein global dimensions for Hopf‎ ‎algebras and twisted smash product algebras $Astar H$‎. ‎Results from‎ ‎the literature are generalized‎. 

NOTES ON REGULAR MULTIPLIER HOPF ALGEBRAS

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition