NDLI: Representations of Hopf-Ore Extensions of Group Algebras and Pointed Hopf Algebras of Rank One

Content Provider	Springer Nature Link
Author	Chen, Hui Xiang Wang, Zhen You, Lan
Copyright Year	2015
Abstract	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 ′.
Ending Page	830
Page Count	30
Starting Page	801
File Format	PDF
ISSN	1386923X
e-ISSN	15729079
Journal	Algebras and Representation Theory
Issue Number	3
Volume Number	18
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-01-28
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Associative Rings and Algebras Non-associative Rings and Algebras Pointed Hopf algebra Hopf-Ore extension Simple module Commutative Rings and Algebras Indecomposable module Weight module Representations of orders, lattices, algebras over commutative rings
Content Type	Text
Resource Type	Article
Subject	Mathematics

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