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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 5, Pages 1015–1025
DOI: https://doi.org/10.17377/smzh.2017.58.505 (Mi smj2915) 		 
Lie algebras induced by a nonzero field derivation

A. G. Gein

Ural Federal University, Ekaterinburg, Russia
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DOI: https://doi.org/10.17377/smzh.2017.58.505
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 $\operatorname{char}F>3$; then the corresponding algebra is simple, presenting a nonisomorphic analog of the Zassenhaus algebra $W_1(m)$.
Keywords: simple Lie algebra, field derivation, Zassenhaus algebra, $A$-algebra.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
The author was supported by the Government of the Russian Federation Program and Ural Federal University (Grant 02.A03.21.0006 on 27.08.2013).
Received: 15.09.2016
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 5, Pages 786–793
DOI: https://doi.org/10.1134/S0037446617050056
Bibliographic databases:
Document Type: Article
UDC: 512.55
MSC: 35R30
Language: Russian
Citation: A. G. Gein, “Lie algebras induced by a nonzero field derivation”, Sibirsk. Mat. Zh., 58:5 (2017), 1015–1025; Siberian Math. J., 58:5 (2017), 786–793
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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