The Grothendieck Group of Hopf Algebras

Algebraic Structures on Grothendieck Groups of a Tower of Algebras

The Grothendieck group of the tower of symmetric group algebras has a self-dual graded Hopf algebra structure. Inspired by this, we introduce by way of axioms, a general notion of a tower of algebras and study two Grothendieck groups on this tower linked by a natural paring. Using representation theory, we show that our axioms give a structure of graded Hopf algebras on each Grothendieck groups...

On a quantum analog of the Grothendieck-Teichmüller group

We introduce a self-dual, noncommutative, and noncocommutative Hopf algebra HGT which takes for certain Hopf categories (and therefore braided monoidal bicategories) a similar role as the GrothendieckTeichmüller group for quasitensor categories. We also give a result which highly restricts the possibility for similar structures for higher weak n-categories (n ≥ 3) by showing that these structur...

On the Coderivations of Some Hopf Algebras

On Associators and the Grothendieck - Teichmuller

We present a formalism within which the relationship (discovered by Drinfel’d in [Dr1, Dr2]) between associators (for quasi-triangular quasi-Hopf algebras) and (a variant of) the Grothendieck-Teichmuller group becomes simple and natural, leading to a great simplification of Drinfel’d’s original work. In particular, we re-prove that rational associators exist and can be constructed iteratively.

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