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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 467–477
DOI: https://doi.org/10.17377/semi.2016.13.040
(Mi semr690)
 

This article is cited in 8 scientific papers (total in 8 papers)

Mathematical logic, algebra and number theory

Hypercentral automorphisms of nil-triangular subalgebras in Chevalley algebras

V. M. Levchuk, A. V. Litavrin

Inst. Math. and Found. Inform. of Siberian Federal University, Pr. Svobodny, 79, 660041, Krasnoyarsk, Russia
Full-text PDF (177 kB) Citations (8)
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Abstract: 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, nil-triangular subalgebra, height of hypercentral automorphism.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00707_а
Received February 26, 2016, published June 7, 2016
Bibliographic databases:
Document Type: Article
UDC: 512.554
MSC: 16R40,17D99
Language: Russian
Citation: V. M. Levchuk, A. V. Litavrin, “Hypercentral automorphisms of nil-triangular subalgebras in Chevalley algebras”, Sib. Èlektron. Mat. Izv., 13 (2016), 467–477
Citation in format AMSBIB
\Bibitem{LevLit16}
\by V.~M.~Levchuk, A.~V.~Litavrin
\paper Hypercentral automorphisms of nil-triangular subalgebras in Chevalley algebras
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 467--477
\mathnet{http://mi.mathnet.ru/semr690}
\crossref{https://doi.org/10.17377/semi.2016.13.040}
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  • This publication is cited in the following 8 articles:
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