Automorphism group of Green ring of Sweedler Hopf algebra

Let H2 be Sweedler＇s 4-dimensional Hopf algebra and r（H2） be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r（H2） and Green algebra F（H2） = r（H2） zF, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism g...

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Published in	Frontiers of Mathematics Vol. 11; no. 4; pp. 921 - 932
Main Authors	JIA, Tingting, ZHAO, Ruju, LI, Libin
Format	Journal Article
Language	English
Published	Beijing Higher Education Press 01.08.2016 Springer Nature B.V
Subjects	Algebra Automorphism group Automorphisms Green algebra Green ring Hopf代数 Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Multiplication Research Article Rings (mathematics) Studies Sweedler Hopf algebra Theorems 乘法克莱因半直积四维氢自同构群 Automorphism group 19A22 Green ring Sweedler Hopf algebra 16W20 Green algebra
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ISSN	1673-3452 2731-8648 1673-3576 2731-8656
DOI	10.1007/s11464-016-0565-4

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Summary:	Let H2 be Sweedler＇s 4-dimensional Hopf algebra and r（H2） be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r（H2） and Green algebra F（H2） = r（H2） zF, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r（H2） is isomorphic to K4, where K4 is the Klein group, and the automorphism group of F（H2） is the semidirect product of Z2 and G, where G = F ／ {1/2} with multiplication given by a. b = 1 - a - b ＋ 2ab.
Bibliography:	Let H2 be Sweedler＇s 4-dimensional Hopf algebra and r（H2） be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r（H2） and Green algebra F（H2） = r（H2） zF, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r（H2） is isomorphic to K4, where K4 is the Klein group, and the automorphism group of F（H2） is the semidirect product of Z2 and G, where G = F ／ {1/2} with multiplication given by a. b = 1 - a - b ＋ 2ab. Automorphism group, Green ring, Green algebra, Sweedler Hopf algebra 11-5739/O1 Document accepted on :2015-12-05 Automorphism group Green ring Sweedler Hopf algebra Green algebra Document received on :2015-09-25 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	1673-3452 2731-8648 1673-3576 2731-8656
DOI:	10.1007/s11464-016-0565-4