The Automorphism Group of Green Algebra of 9-Dimensional Taft Hopf Algebra
The Automorphism Group of Green Algebra of 9-Dimensional Taft Hopf Algebra
复制标题
9维Taft Hopf代数的绿色代数自同构群
DOI：
10.1142/s1005386720000656
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发表时间：
2020-12
影响因子：
0.3
通讯作者：
Li Libin
中科院分区：
文献类型：
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作者：
Zhao Ruju;Yuan Chengtao;Li Libin
设H_3是9维Taft-Hopf代数，r(H_3)是H_3的对应格林环，Aut(R(H_3))是实数域R上的格林代数R(H_3)=R⊗Z r(H_3)的自同构群，我们证明了商群Aut(R(H_3))/T_1同构于12阶二面体群与2阶循环群的直积，其中T_1是包含单位映射的同构类，同构于群G={(c，d)∈R~2|(c，d)6=(-1/3，-1/6)}，乘法由(c_1，d_1)·(c_2，d_2)=(c_1+c_2+2c_1c_2-4d_1d_2+2c_1d_2+2d_1c_2给出，D1+d2-2c1c2-2d1d2+4c1d2+4d1c2)。
Let H_3 be the 9-dimensional Taft Hopf algebra, let r(H_3) be the corresponding Green ring of H_3, and let Aut(R (H_3)) be the automorphism group of Green algebra R (H_3) = R ⊗ Z r(H_3) over the real number field R. We prove that the quotient group Aut(R (H_3))/T_1 is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2, where T_1 is the isomorphism class which contains the identity map and is isomorphic to a group G = {(c, d) ∈ R~2 | (c, d) 6= (-1/3, -1/6)} with multiplication given by (c_1, d_1) ·(c_2, d_2) = (c_1+c_2+2c_1 c_2-4d_1 d_2+2c_1 d_2+2d_1 c_2, d_1+d_2-2c_1 c_2-2d_1 d_2+4c_1 d_2+4d_1 c_2).