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

• 作者: Ruju Zhao Chengtao Yuan Libin Li
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 767-798
• 页数: 32页
• 语种: 英文
• DOI: 10.1142/S1005386720000656

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 ×z r(H3) over the real number field R.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) ∈ R2|(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).