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DC Field | Value | Language |
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dc.contributor.author | WANG, Zhihua | - |
dc.contributor.author | Li, Libin | - |
dc.contributor.author | ZHANG, Yinhuo | - |
dc.date.accessioned | 2016-01-13T14:23:41Z | - |
dc.date.available | 2016-01-13T14:23:41Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | JOURNAL OF ALGEBRA, 449, p. 108-137 | - |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.uri | http://hdl.handle.net/1942/20229 | - |
dc.description.abstract | In this paper, we continue our study of the Green rings of finite dimensional pointed Hopf algebras of rank one initiated in [22], but focus on those Hopf algebras of non-nilpotent type. Let H be a finite dimensional pointed rank one Hopf algebra of non-nilpotent type. We first determine all non-isomorphic indecomposable H -modules and describe the Clebsch–Gordan formulas for them. We then study the structures of both the Green ring r(H) and the Grothendieck ring G0(H) of H and establish the precise relation between the two rings. We use the Cartan map of H to study the Jacobson radical and the idempotents of r(H). It turns out that the Jacobson radical of r(H) is exactly the kernel of the Cartan map, a principal ideal of r(H), and r(H) has no non-trivial idempotents. Besides, we show that the stable Green ring of H is a transitive fusion ring. This enables us to calculate Frobenius–Perron dimensions of objects in the stable category of H. Finally, as an example, we present both the Green ring and the Grothendieck ring of the Radford Hopf algebra in terms of generators and relations. | - |
dc.description.sponsorship | The first author is supported by Natural Science Foundation of Jiangsu Province of China (No. BK20150537) and Natural Science Foundation of Jiangsu Higher Education Institution of China (No. 15KJB110013). The second author is supported by SRFDP of China (No. 20123250110005) and NSF of China (No. 11471282). The third author is supported by FWO (Grant No. G029411). | - |
dc.language.iso | en | - |
dc.rights | © 2015 Elsevier Inc. All rights reserved. | - |
dc.subject.other | green ring; indecomposable module; pointed rank one Hopf algebra; Jacobson radical; Frobenius–Perron dimension | - |
dc.title | Green rings of pointed rank one Hopf algebras of non-nilpotent type | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 137 | - |
dc.identifier.spage | 108 | - |
dc.identifier.volume | 449 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Wang, ZH (reprint author), Nanjing Normal Univ, Taizhou Coll, Dept Math, Taizhou 225300, Peoples R China. mafzhua@126.com; lbli@yzu.edu.cn; yinhuo.zang@hassolt.bo | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1016/j.jalgebra.2015.11.002 | - |
dc.identifier.isi | 000375634600004 | - |
item.fullcitation | WANG, Zhihua; Li, Libin & ZHANG, Yinhuo (2016) Green rings of pointed rank one Hopf algebras of non-nilpotent type. In: JOURNAL OF ALGEBRA, 449, p. 108-137. | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2017 | - |
item.contributor | WANG, Zhihua | - |
item.contributor | Li, Libin | - |
item.contributor | ZHANG, Yinhuo | - |
item.accessRights | Restricted Access | - |
crisitem.journal.issn | 0021-8693 | - |
crisitem.journal.eissn | 1090-266X | - |
Appears in Collections: | Research publications |
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Green Rings of Pointed Rank One Hopf Algebras of non-Nilpotent Type.pdf Restricted Access | Published version | 526.53 kB | Adobe PDF | View/Open Request a copy |
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