Geodesic
Hypercentral automorphisms of nil-triangular subalgebras in Chevalley algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 467-477

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Let $N\Phi(K)$ be the nil-triangular subalgebra of the Chevalley algebra over an associative commutative ring $K$ with the identity associated with a root system $\Phi$. (All elements $e_r \in \Phi^+$ of Chevalley basis give its basis.) We study automorphisms of the Lie ring $N\Phi(K)$; this problem is closely related to the modeltheoretic study of Lie rings $N\Phi(K)$. Our main theorem shows that the largest height of hypercentral automorphisms of $N\Phi(K)$ is bounded by a constant, except orthogonal cases $B_n$ and $D_n$, when $2K\neq K$.
Keywords: Chevalley algebra, height of hypercentral automorphism.
Mots-clés : nil-triangular subalgebra 
@article{SEMR_2016_13_a14,
     author = {V. M. Levchuk and A. V. Litavrin},
     title = {Hypercentral automorphisms of nil-triangular subalgebras in {Chevalley} algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {467--477},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a14/}
}
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V. M. Levchuk; A. V. Litavrin. Hypercentral automorphisms of nil-triangular subalgebras in Chevalley algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 467-477. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a14/