Frontiers of Mathematics in China >
Automorphism group of Green ring of Sweedler Hopf algebra
Received date: 25 Sep 2015
Accepted date: 05 Dec 2015
Published date: 30 Aug 2016
Copyright
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) ⊗, 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 2 and G, where G= F \ {1/2} with multiplication given by a · b= 1− a − b+ 2ab.
Key words: Automorphism group; Green ring; Green algebra; Sweedler Hopf algebra
Tingting JIA , Ruju ZHAO , Libin LI . Automorphism group of Green ring of Sweedler Hopf algebra[J]. Frontiers of Mathematics in China, 2016 , 11(4) : 921 -932 . DOI: 10.1007/s11464-016-0565-4
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