Nilpotency of \(n\)-tuple Lie algebras and associative \(n\)-tuple algebras (Q847880)

The author finds conditions for the nilpotency of finite-dimensional \(n\)-tuple Lie algebras and finite-dimensional associative \(n\)-tuple algebras. The conditions are analogous to theorems of Engel and Wedderburn for Lie algebras and associative algebras. The structure of \(n\)-tuple algebras of associative type was investigated by the author in [Russ. Math. 52, No. 12, 28--35 (2008); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2008, No. 12, 34--42 (2008; Zbl 1207.17009)], and the structure of symmetric 2-tuple Lie algebras was studied in [\textit{V. V. Dotsenko} and \textit{A. S. Khoroshkin}, Funct. Anal. Appl. 41, No. 1, 1--17 (2007); translation from Funkts. Anal. Prilozh. 41, No. 1, 1--22 (2007; Zbl 1145.18001)].