Geodesic
Automorphisms of nil-triangular subrings of chevalley algebras of type $G_2$ over the field of characteristic $2$
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 88 (2024), pp. 26-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $N\Phi(K)$ be a niltriangular subalgebra of the Chevalley algebra of an associative-commutative ring $K$ with identity, associated with the root system $\Phi$ (the basis $N\Phi(K)$ consists of all elements $e_r\in\Phi^+$ of the Chevalley basis). We describe automorphisms of a niltriangular Lie ring of type $G_2$ over a field $K$ under the constraint $2K=0$. To study automorphisms, the upper and lower central series described in this paper are essentially used.
Keywords: Chevalley algebra, ring, hypercentral automorphism.
Mots-clés : nil-triangular subalgebra, automorphism 
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A. V. Kazakova. Automorphisms of nil-triangular subrings of chevalley algebras of type $G_2$ over the field of characteristic $2$. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 88 (2024), pp. 26-36. http://geodesic.mathdoc.fr/item/VTGU_2024_88_a2/

[1] Levchuk V.M., “Connections between a unitriangular group and certain rings. Chapter 2: Groups of automorphisms”, Siberian Mathematical Journal, 24 (1983), 543–557 | DOI

[2] Cao Y., Jiang D., Wang J., “Automorphisms of certain nilpotent Lie algebras over commutative rings”, Intern. J. Algebra and Computation, 17:3 (2007), 527–555 | DOI

[3] Levchuk V.M., “Automorphisms of unipotent subgroups of Chevalley groups”, Algebra and Logic, 29 (1990), 211–224 | DOI

[4] Litavrin A.V., “Automorphisms of the nilpotent subalgebra $N\Phi(K)$ of the Chevalley algebra of symplectic type”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika - The Bulletin of Irkutsk State University. Series Mathematics, 13:3 (2015), 41–55

[5] Levchuk V.M., Litavrin A.V., “Hypercentral automorphisms of nil-triangular subalgebras in Chevalley algebras”, Siberian Electronic Mathematical Reports, 13 (2016), 467–477 | DOI

[6] Litavrin A.V., Automorphisms of nil-triangular subrings of Chevalley algebras of classic types, Dissertation, Siberian Federal University, 2017

[7] Kazakova A.V., “Automorphisms of the nil-triangular subring of the Chevalley algebra of type $G_2$”, Collection of papers of the All-Russia Young Researchers' Scientific Conference “All Faces of Mathematics” (Tomsk, 2022), Krasnoye Znamya, Tomsk, 2022, 28

[8] Carter R., Simple Groups of Lie Type, Wiley and Sons, New York, 1972, 331 pp.

[9] Kazakova A.V., Kirillova E.A., “Automorphisms and central series of niltriangular subrings of Chevalley algebras”, Collection of Abstracts of the International Conference “Mal'tsev Meeting” (Novosibirsk, 2020), Novosibirsk State University, Novosibirsk, 2020, 191

[10] Gibbs J.A., “Automorphisms of certain unipotent groups”, J. Algebra, 14:2 (1970), 203–208 | DOI

[11] Levchuk V.M., Litavrin A.V., “Automorphisms of nil-triangular subrings of Chevalley algebras of orthogonal types”, Vestnik sibirskogo gosudarstvennogo aerokosmicheskogo uni versiteta imeni Akademika M.F. Reshetneva - Siberian Aerospace Journal, 17:2 (2016), 324–327

[12] Kuzucuoglu F., Levchuk V.M., “The automorphism group of certain radical rings”, Journal of Algebra, 243 (2001), 473–485 | DOI