alexa Nilpotency of Zinbiel Algebras


Journal of Generalized Lie Theory and Applications

Author(s): A S DzhumadilDaev, K M Tulenbaev

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Zinbiel algebras are defined by the identity (a ∘ b) ∘ c = a∘(b∘c+c∘b). We prove an analog of the Nagata–Higman theorem for Zinbiel algebras. We establish that every finite-dimensional Zinbiel algebra over an algebraically closed field is solvable. Every solvable Zinbiel algebra with solvability length N is a nil-algebra with nil-index 2N if p = char K = 0 or p > 2N − 1. Conversely, every Zinbiel nil-algebra with nil-index N is solvable with solvability length N if p = 0 or p > N − 1. Every finite-dimensional Zinbiel algebra over complex numbers is nilpotent, nil, and solvable.

This article was published in Journal of Dynamical and Control Systems and referenced in Journal of Generalized Lie Theory and Applications

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