Relative PBW Type Theorems for Symmetrically Braided Hopf Algebras

Braided Hopf algebras of triangular type

Integrals for braided Hopf algebras

Let H be a Hopf algebra in a rigid braided monoidal category with split idempotents. We prove the existence of integrals on (in) H characterized by the universal property, employing results about Hopf modules, and show that their common target (source) object IntH is invertible. The fully braided version of Radford’s formula for the fourth power of the antipode is obtained. Connections of integ...

Braided Hopf Algebras

Preface The term " quantum group " was popularized by Drinfeld in his address to the International Congress of Mathematicians in Berkeley. However, the concepts of quantum groups and quasitriangular Hopf algebras are the same. Therefore, Hopf algebras have close connections with various areas of mathematics and physics. The development of Hopf algebras can be divided into five stages. The first...

Pbw Deformations of Braided Symmetric Algebras and a Milnor-moore Type Theorem for Braided Bialgebras

Braided bialgebras were defined by mimicking the definition of bialgebras in a braided category; see [Ta]. In this paper we are interested in those braided bialgebras that are connected as a coalgebra, and such that, up to multiplication by a certain scalar, their braiding restricted to the primitive part is a Hecke operator. To every braided bialgebra as above we associate a braided Lie algebr...

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.