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Engel’s theorem for algebras of Lie type. (English, Russian) Zbl 1193.17005

Russ. Math. 49, No. 7, 28-34 (2005); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2005, No. 7, 30-36 (2005).
In this paper the author proves an analog of Engel’s Theorem for finite-dimensional nonassociative algebras of Lie type. The simplest examples of those algebras were defined in papers by Yu. A. Bakhturin and M. V. Zaitsev [J. Algebra 205, No. 1, 1–12 (1998; Zbl 0920.16011)] and by Bakhturin, Zaitsev and S. K. Sehgal [Sb. Math. 190, No. 11, 1559–1570 (1999); translation from Mat. Sb. 190, No. 11, 3–14 (1999; Zbl 0939.17002)]. The Engel Theorem is applied to prove the existence of the Cartan subalgebras in these algebras.

MSC:

17A99 General nonassociative rings
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