The Automorphism Group of Green Algebra of 9-Dimensional Taft Hopf Algebra  

作　　者：Ruju Zhao Chengtao Yuan Libin Li 

机构地区：[1]College of Science,Beibu Gulf University,Qinzhou,Guangxi 535011,China [2]School of Mathematics and Statistics,Huaiyin Normal University Huai'an,Jiangsu 223300,China [3]School of Mathematical Science,Yangzhou University,Yangzhou,Jiangsu 225002,China

出　　处：《Algebra Colloquium》2020年第4期767-798,共32页代数集刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Nos.11661014,11701499,11871063,and 11711530703);the Research Innovation Program Project of Academic Degree Graduate Students in Jiangsu(XKYCX17_029);the Excellent Doctoral Dissertation Foundation Project of Yangzhou University in 2018.

摘　　要：Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the quotient group Aut(R(H3))/T1 is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2,where T1 is the isomorphism class which contains the identity map and is isomorphic to a group G={(c,d)∈R^(2)∣∣(c,d)≠(−1/3,−1/6)}with multiplication given by(c1,d1)⋅(c2,d2)=(c1+c2+2c1c2−4d1d2+2c1d2+2d1c2,d1+d2−2c1c2−2d1d2+4c1d2+4d1c2).

关 键 词：auto morphism group Green ring Green algebra 9-dimensional Taft Hopf algebra 

分 类 号：O15[理学—数学]