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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - A. N. Grishkov
AU  - M. N. Rasskazova
TI  - Automorphism groups of diagonal $\mathbf Z_p$-forms of the Lie algebra $sl_2(\mathbf Q_p)$, $p>2$
JO  - Algebra i logika
PY  - 2017
SP  - 406
EP  - 420
VL  - 56
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2017_56_4_a1/
LA  - ru
ID  - AL_2017_56_4_a1
ER  - 
%0 Journal Article
%A A. N. Grishkov
%A M. N. Rasskazova
%T Automorphism groups of diagonal $\mathbf Z_p$-forms of the Lie algebra $sl_2(\mathbf Q_p)$, $p>2$
%J Algebra i logika
%D 2017
%P 406-420
%V 56
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2017_56_4_a1/
%G ru
%F AL_2017_56_4_a1
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/

[1] N. Dzhekobson, Algebry Li, Mir, M., 1964 | MR

[2] A. V. Yuschenko, “Formy i predstavleniya algebry Li $sl_2(\mathbb Z)$”, Sib. matem. zh., 43:5 (2002), 1197–1207 | MR | Zbl

[3] A. N. Grishkov, “Predstavleniya koltsa Li $sl_2(\mathbb Z)$ nad koltsom tselykh chisel”, Sib. matem. zh., 41:6 (2000), 1338–1344 | MR | Zbl