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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Loday J.-L., “Une version non commutative des algebres de Lie: Les algebres de Leibniz,” Enseign. Math., 39,No. 3–4, 269-293 (1993).
Loday J.-L. and Pirashvili T., “Universal enveloping algebras of Leibniz algebras and (co)homology,” Math. Ann., 296,No. 1, 139-158 (1993).
Mal'tsev A. I., Foundations of Linear Algebra [in Russian], Nauka, Moscow (1970).
Albeverio S., Ayupov Sh. A., and Omirov B. A., “On nilpotent and simple Leibniz algebras,” Comm. Algebra, 2004 (to appear).
Jacobson N., Lie Algebras [Russian translation], Mir, Moscow (1964).
Abdykassymova S. and Dzhumadil'daev A., “Simple Leibniz algebras of rank 1,” in: Abstracts: IX Intern. Conf. of the Representation Theory of Algebras, Beijing (China), 2000, pp. 17-18.
Rights and permissions
About this article
Cite this article
Ayupov, S.A., Omirov, B.A. The Nilpotency Properties of the Leibniz Algebra Mn(C)D . Siberian Mathematical Journal 45, 399–409 (2004). https://doi.org/10.1023/B:SIMJ.0000028604.91651.80
Issue Date:
DOI: https://doi.org/10.1023/B:SIMJ.0000028604.91651.80