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The nilpotency properties of the Leibniz algebra \(M_n(\mathbb C)_D\). (Russian, English) Zbl 1059.17002

Sib. Mat. Zh. 45, No. 3, 483-496 (2004); translation in Sib. Math. J. 45, No. 3, 399-409 (2004).
Let \(A\) be an associative algebra, let \(D\) be a linear transformation of \(A\) such that \(D(a(Db))=D(a)D(b)=D((Da)b)\), and let \([a,b]_D:=a(Db)-D(b)a\) for all \(a,b\in A\). Then \(A_D=(A,[\cdot,\cdot]_D)\) is a Leibniz algebra. The authors study the Leibniz algebras \(M_n(\mathbb C)_D\). The main result of the article is a nilpotency criterion obtained for these algebras.

MSC:

17A32 Leibniz algebras
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