Geodesic
Automorphism groups of diagonal $\mathbf Z_p$-forms of the Lie algebra $sl_2(\mathbf Q_p)$, $p>2$
Algebra i logika, Tome 56 (2017) no. 4, pp. 406-420

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A. V. Yushchenko's paper [Sib. Mat. Zh., 43, No. 5, 1197–1207] implies that two nondiagonal forms like $S(n,d)+\mathbf Z_pA$ and $S(n,d)+\mathbf Z_pA'$ are isomorphic if the elements of $A$ and $A'$ are conjugated via the group $\mathrm{Aut}_{\mathbf Z_p}S(n,d)$. In the present paper, we settle just this question on conjugation. In other words, we describe the group $\mathrm{Aut}_{\mathbf Z_p}S(n,d)$ and clarify under which conditions two elements of $S(n,d)$ are conjugate under the action of this group on $S(n,d)$, $p>2$.
Keywords: Lie algebra, diagonal $\mathbf Z_p$-form
Mots-clés : automorphism group. 
@article{AL_2017_56_4_a1,
     author = {A. N. Grishkov and M. N. Rasskazova},
     title = {Automorphism groups of diagonal $\mathbf Z_p$-forms of the {Lie} algebra $sl_2(\mathbf Q_p)$, $p>2$},
     journal = {Algebra i logika},
     pages = {406--420},
     publisher = {mathdoc},
     volume = {56},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_4_a1/}
}
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A. N. Grishkov; M. N. Rasskazova. Automorphism groups of diagonal $\mathbf Z_p$-forms of the Lie algebra $sl_2(\mathbf Q_p)$, $p>2$. Algebra i logika, Tome 56 (2017) no. 4, pp. 406-420. http://geodesic.mathdoc.fr/item/AL_2017_56_4_a1/