Hopf Algebras with Positive Bases

Quasi-triangular structures on Hopf algebras with positive bases

A basis B of a finite dimensional Hopf algebra H is said to be positive if all the structure constants of H relative to B are non-negative. A quasi triangular structure R ∈ H ⊗ H is said to be positive with respect to B if it has non-negative coefficients in the basis B ⊗ B of H ⊗ H. In our earlier work, we have classified all finite dimensional Hopf algebras with positive bases. In this paper,...

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

On the Coderivations of Some Hopf Algebras

2 7 N ov 2 00 3 PBW bases for a class of braided Hopf algebras ⋆

We prove the existence of a basis of Poincaré-Birkhoff-Witt type for braided Hopf algebras R generated by a braided subspace V ⊂ P (R) if the braiding on V fulfils a triangularity condition. We apply our result to pointed Hopf algebras with abelian coradical and to Nichols algebras of low dimensional simple Uq(sl2)-modules.

Yang-baxter Bases of 0-hecke Algebras and Representation Theory of 0-ariki-koike-shoji Algebras

After reformulating the representation theory of 0-Hecke algebras in an appropriate family of Yang-Baxter bases, we investigate certain specializations of the Ariki-Koike algebras, obtained by setting q = 0 in a suitably normalized version of Shoji’s presentation. We classify the simple and projective modules, and describe restrictions, induction products, Cartan invariants and decomposition ma...