caa a22 4500 606160868 CHVBK 20210128100632.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10468-015-9517-z doi (NATIONALLICENCE)springer-10.1007/s10468-015-9517-z Representations of Hopf-Ore Extensions of Group Algebras and Pointed Hopf Algebras of Rank One [Elektronische Daten] [Zhen Wang, Lan You, Hui-Xiang Chen] 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 k. Let H=k G(χ,a,δ) be a Hopf-Ore extension of k G and H ′ a rank one quotient Hopf algebra of H, where k is a field, G is a group, a is a central element of G and χ is a k-valued character for G with χ(a)≠1. We first show that the simple weight modules over H and H ′ are finite dimensional. Then we describe the structures of all simple weight modules over H and H ′, and classify them. We also consider the decomposition of the tensor product of two simple weight modules over H ′ into the direct sum of indecomposable modules. Furthermore, we describe the structures of finite dimensional indecomposable weight modules over H and H ′, and classify them. Finally, when χ(a) is a primitive n-th root of unity for some n≥2, we determine all finite dimensional indecomposable projective objects in the category of weight modules over H ′. Springer Science+Business Media Dordrecht, 2015 Pointed Hopf algebra nationallicence Hopf-Ore extension nationallicence Weight module nationallicence Simple module nationallicence Indecomposable module nationallicence Wang Zhen Department of Fundamental Sciences, Yancheng Institute of Technology, 224051, Yancheng, China aut You Lan Department of Fundamental Sciences, Yancheng Institute of Technology, 224051, Yancheng, China aut Chen Hui-Xiang School of Mathematical Science, Yangzhou University, 225002, Yangzhou, China aut Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 801-830 1386-923X 18:3<801 2015 18 10468 https://doi.org/10.1007/s10468-015-9517-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9517-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Zhen Department of Fundamental Sciences, Yancheng Institute of Technology, 224051, Yancheng, China aut NATIONALLICENCE 700 1- You Lan Department of Fundamental Sciences, Yancheng Institute of Technology, 224051, Yancheng, China aut NATIONALLICENCE 700 1- Chen Hui-Xiang School of Mathematical Science, Yangzhou University, 225002, Yangzhou, China aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 801-830 1386-923X 18:3<801 2015 18 10468