Automorphism Groups of Diagonal Zp-Forms of the Lie Algebra sl2(Qp), p > 2

Abstract

It follows from [2] that two nondiagonal forms like S(n, d) + Z_pA and S(n, d) + Z_pA^′ are isomorphic if the elements of A and A′ are conjugated via the group \( {\mathrm{Aut}}_{{\boldsymbol{Z}}_p}S\left(n,d\right) \). In the present paper, we settle just this question on conjugation. In other words, we describe the group \( {\mathrm{Aut}}_{{\boldsymbol{Z}}_p}S\left(n,d\right) \) and clarify under which conditions two elements of S(n, d) are conjugate under the action of this group on S(n, d), p > 2.