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Lie algebras induced by a nonzero field derivation

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Abstract

Given a finite-dimensional associative commutative algebra A over a field F, we define the structure of a Lie algebra using a nonzero derivation D of A. If A is a field and charF > 3; then the corresponding algebra is simple, presenting a nonisomorphic analog of the Zassenhaus algebra W 1(m).

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Authors and Affiliations

  1. Ural Federal University, Ekaterinburg, Russia

    A. G. Gein

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  1. A. G. Gein
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Correspondence to A. G. Gein.

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Original Russian Text Copyright © 2017 Gein A.G.

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 5, pp. 1015–1026, September–October, 2017; DOI: 10.17377/smzh.2017.58.505.

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Gein, A.G. Lie algebras induced by a nonzero field derivation. Sib Math J 58, 786–793 (2017). https://doi.org/10.1134/S0037446617050056

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  • DOI: https://doi.org/10.1134/S0037446617050056

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