Hopf algebras under finiteness conditions

Projectivity of Hopf algebras over subalgebras with semilocal central localizations

Let H be a Hopf algebra over a field k and A a right coideal subalgebra of H , that is, A is a subalgebra satisfying ∆(A) ⊂ A⊗H where ∆ is the comultiplication in H . In case when H is finitely generated commutative, the right coideal subalgebras are intimately related to the homogeneous spaces for the corresponding group scheme. The purpose of this paper is to extend the class of pairsA,H for ...

Classification of arithmetic root systems

Arithmetic root systems are invariants of Nichols algebras of diagonal type with a certain finiteness property. They can also be considered as generalizations of ordinary root systems with rich structure and many new examples. On the other hand, Nichols algebras are fundamental objects in the construction of quantized enveloping algebras, in the noncommutative differential geometry of quantum g...

On the Coderivations of Some Hopf Algebras

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

Skew Derivations and Deformations of Algebras

We obtain deformations of a crossed product of a polynomial algebra with a group, under some conditions, from universal deformation formulas. These formulas arise from actions of Hopf algebras generated by automorphisms and skew derivations. They are universal in the sense that they apply to deform all algebras with such Hopf algebra actions, and we give one additional example.