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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
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.
Received February 26, 2016, published June 7, 2016
Citation:
V. M. Levchuk, A. V. Litavrin, “Hypercentral automorphisms of nil-triangular subalgebras in Chevalley algebras”, Sib. Èlektron. Mat. Izv., 13 (2016), 467–477
Linking options:
https://www.mathnet.ru/eng/semr690 https://www.mathnet.ru/eng/semr/v13/p467
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