Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 4: 921 - 932

DOI: 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
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  • School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

Received date: 25 Sep 2015

Accepted date: 05 Dec 2015

Published date: 30 Aug 2016

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Automorphism group; Green ring; Green algebra; Sweedler Hopf algebra

Cite this article

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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