Automorphism group of Green ring of Sweedler Hopf algebra

doi:10.1007/s11464-016-0565-4

Front. Math. China

2016, Vol. 11

Issue (4) : 921-932 https://doi.org/10.1007/s11464-016-0565-4

RESEARCH ARTICLE

Automorphism group of Green ring of Sweedler Hopf algebra

Tingting JIA,Ruju ZHAO,Libin LI(

)

School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

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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) ⊗FZ, 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.

Keywords Automorphism group Green ring Green algebra Sweedler Hopf algebra

Corresponding Author(s): Libin LI

Issue Date: 30 August 2016

Cite this article:

Tingting JIA,Ruju ZHAO,Libin LI. Automorphism group of Green ring of Sweedler Hopf algebra[J]. Front. Math. China, 2016, 11(4): 921-932.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0565-4
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I4/921

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