Abstract
We obtain conditions for the nilpotency of finite-dimensional n-tuple Lie algebras and finite-dimensional associative n-tuple algebras. The established conditions are analogous to theorems of Engel and Wedderburn for Lie algebras and associative algebras.
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N. A. Koreshkov, “n-Tuple Algebras of Associative Type,” Izv. Vyssh. Uchebn. Zaved. Mat.,No. 12, pp. 34–42 (2008) [Iz. VUZ (Russian Mathematis) 52 (12), 28–35 (2008)].
V. V. Dotsenko and A. S. Khoroshkin, “Character Formulas for the Operad of Two Compatible Brackets and for the Bi-Hamiltonian Operad,” Funkts. Analiz i Ego Prilozh. 41(1), 1–22 (2007).
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Original Russian Text © N.A. Koreshkov, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 2, pp. 33–38.
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Koreshkov, N.A. Nilpotency of n-tuple Lie algebras and associative n-tuple algebras. Russ Math. 54, 28–32 (2010). https://doi.org/10.3103/S1066369X10020040
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DOI: https://doi.org/10.3103/S1066369X10020040