8,644 research outputs found
Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one
In this paper, we study the representation theory of Hopf-Ore extensions of
group algebras and pointed Hopf algebras of rank one over an arbitrary field
. Let H=kG(\chi, a,\d) be a Hopf-Ore extension of and a rank one
quotient Hopf algebra of , where is a field, is a group, is a
central element of and is a -valued character for with
. We first show that the simple weight modules over and
are finite dimensional. Then we describe the structures of all simple weight
modules over and , and classify them. We also consider the
decomposition of the tensor product of two simple weight modules over into
the direct sum of indecomposable modules. Furthermore, we describe the
structures of finite dimensional indecomposable weight modules over and
, and classify them. Finally, when is a primitive -th root of
unity for some , we determine all finite dimensional indecomposable
projective objects in the category of weight modules over .Comment: arXiv admin note: substantial text overlap with arXiv:1206.394
- …