This article is cited in 3 papers

The nilpotency properties of the Leibniz algebra $M_n(C)_D$

Sh. A. Ayupov, B. A. Omirov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We study the nilpotency properties of the Leibniz algebras constructed by means of $D$-mappings on the algebra of complex square matrices $M_n(C)$. In particular, we obtain a criterion for nilpotency of these algebras in terms of the properties of a $D$-mapping. We prove also that the Leibniz algebras under consideration cannot be simple.

Keywords: Leibniz algebra, associative algebra, $D$-mapping, nilpotency, simple Leibniz algebra.

UDC: 512.554.38

Received: 18.03.2003

 English version: Siberian Mathematical Journal, 2004, 45:3, 399–409

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