Representations of Hopf-Ore extensions of group algebras

2021/07/15 by Sun, Hua, Chen, Hui-Xiang, Zhang, Yinhuo
#16E05 #16G99 #16T99 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2107.07202

Abstract

In this paper, we study the representations of the Hopf-Ore extensions kG(χ^-1, a, 0) of group algebra kG, where k is an algebraically closed field. We classify all finite dimensional simple kG(χ^-1, a, 0)-modules under the assumption |χ|=∞ and |χ|=|χ(a)|1 odd, and char(k)=0. The Grothendieck ring and the Green ring of the Hopf-Ore extension are described respectively in terms of generators and relations.

Related

• Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one
• Hopf-Ore Extensions and Hopf Algebras of Rank One
• Green ring of the category of weight modules over the Hopf-Ore extensions of group algebras
• Generalized Hopf-Ore extensions
• Connected Hopf algebras and iterated Ore extensions