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Title: | Representations of Hopf-Ore Extensions of Group Algebras | Authors: | SUN, Hua Chen, Hui-Xiang ZHANG, Yinhuo |
Issue Date: | 2022 | Publisher: | SPRINGER | Source: | ALGEBRAS AND REPRESENTATION THEORY, | Status: | Early view | Abstract: | In this paper, we study the representations of the Hopf-Ore extensions kG(chi(-1), a, 0) of group algebra kG, where k is an algebraically closed field. We classify all finite dimensional simple kG(chi(-1), a, 0)-modules under the assumption vertical bar chi vertical bar= infinity and vertical bar chi vertical bar = vertical bar chi(a)vertical bar < infinity respectively, and all finite dimensional indecomposable kG (chi(-1), a, 0)-modules under the assumption that kG is finite dimensional and semisimple, and vertical bar chi vertical bar = vertical bar chi(a)vertical bar. Moreover, we investigate the decomposition rules for the tensor product modules over kG (chi(-)(1) , a, 0) when char (k) = 0. Finally, we consider the representations of some Hopf-Ore extension of the dihedral group algebra kD(n), where n = 2m, m > 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. | Notes: | Sun, H (corresponding author), Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China. huasun@yzu.edu.cn; hxchen@yzu.edu.cn; yinhuo.zhang@uhasselt.be |
Keywords: | Hopf-Ore extension;Simple module;Indecomposable module;Dihedral group;Green ring | Document URI: | http://hdl.handle.net/1942/37649 | ISSN: | 1386-923X | e-ISSN: | 1572-9079 | DOI: | 10.1007/s10468-022-10137-2 | ISI #: | WOS:000810384700001 | Rights: | © The Author(s), under exclusive licence to Springer Nature B.V. 2022 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2023 |
Appears in Collections: | Research publications |
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Representations of Hopf-Ore Extensions of Group Algebras.pdf Restricted Access | Early view | 402.81 kB | Adobe PDF | View/Open Request a copy |
Hopf_ore_ext_202107.pdf | Peer-reviewed author version | 393.04 kB | Adobe PDF | View/Open |
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