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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Abstract	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.
AbstractList	Let H 2 be Sweedler’s 4-dimensional Hopf algebra and r ( H 2 ) be the corresponding Green ring of H 2 . In this paper, we investigate the automorphism groups of Green ring r ( H 2 ) and Green algebra F ( H 2 ) = r ( H 2 )⊗ ℤ F , where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r ( H 2 ) is isomorphic to K 4 , where K 4 is the Klein group, and the automorphism group of F ( H 2 ) is the semidirect product of ℤ 2 and G , where G = F {1/2} with multiplication given by a · b = 1− a − b + 2 ab . Let H 2 be Sweedler's 4-dimensional Hopf algebra and r( H 2) be the corresponding Green ring of H 2. In this paper, we investigate the automorphism groups of Green ring r( H 2) and Green algebra F( H 2) = r( H 2) ⊗ F Z , where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r( H 2) is isomorphic to K 4, where K 4 is the Klein group, and the automorphism group of F( H 2) is the semidirect product of Z 2 and G, where G= F \ {1/2} with multiplication given by a · b= 1− a − b+ 2 ab. Let H 2 be Sweedler's 4-dimensional Hopf algebra and r(H 2) be the corresponding Green ring of H 2. In this paper, we investigate the automorphism groups of Green ring r(H 2) and Green algebra F(H 2) = r(H 2) F, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r(H 2) is isomorphic to K 4, where K 4 is the Klein group, and the automorphism group of F(H 2) is the semidirect product of 2 and G, where G = F {1/2} with multiplication given by a · b = 1- a - b + 2ab. 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. Let H sub(2) be Sweedler's 4-dimensional Hopf algebra and r(H sub(2)) be the corresponding Green ring of H sub(2). In this paper, we investigate the automorphism groups of Green ring r(H sub(2)) and Green algebra F(H sub(2)) = r(H sub(2)) sub() F, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r(H sub(2)) is isomorphic to K sub(4), where K sub(4) is the Klein group, and the automorphism group of F(H sub(2)) is the semidirect product of sub(2) and G, where G = F {1/2} with multiplication given by a . b = 1- a - b + 2ab.
Author	Tingting JIA Ruju ZHAO Libin LI
AuthorAffiliation	School of Mathematical Science, Yangzhou University, Yangzhou 225002, China
Author_xml	– sequence: 1 givenname: Tingting surname: JIA fullname: JIA, Tingting organization: School of Mathematical Science, Yangzhou University, Yangzhou 225002, China – sequence: 2 givenname: Ruju surname: ZHAO fullname: ZHAO, Ruju organization: School of Mathematical Science, Yangzhou University, Yangzhou 225002, China – sequence: 3 givenname: Libin surname: LI fullname: LI, Libin email: lbli@yzu.edu.cn organization: School of Mathematical Science, Yangzhou University, Yangzhou 225002, China
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Cites_doi	10.1016/j.jalgebra.2008.08.026 10.1090/S0002-9939-2013-11823-X 10.1073/pnas.68.11.2631 10.1090/conm/585/11618 10.1016/j.jalgebra.2003.12.019 10.1016/0022-4049(79)90027-6
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Notes	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
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Snippet	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... Let H 2 be Sweedler's 4-dimensional Hopf algebra and r( H 2) be the corresponding Green ring of H 2. In this paper, we investigate the automorphism groups of... Let H 2 be Sweedler’s 4-dimensional Hopf algebra and r ( H 2 ) be the corresponding Green ring of H 2 . In this paper, we investigate the automorphism groups... Let H 2 be Sweedler's 4-dimensional Hopf algebra and r(H 2) be the corresponding Green ring of H 2. In this paper, we investigate the automorphism groups of... Let H sub(2) be Sweedler's 4-dimensional Hopf algebra and r(H sub(2)) be the corresponding Green ring of H sub(2). In this paper, we investigate the...
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SubjectTerms	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
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Title	Automorphism group of Green ring of Sweedler Hopf algebra
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