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arXiv · 1710.08141

Classification of algebras of level two in the variety of nilpotent algebras and Leibniz algebras

James Francese·Abror Khudoyberdiyev·Bennett Rennier·Anastasia Voloshinov
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Abstract

This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the variety of Leibniz algebras. It is shown that, up to isomorphism, there exist three Leibniz algebras of level two, one of which is solvable, and two of which are nilpotent. Moreover we describe all algebras of level two in the variety of nilpotent algebras.

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James Francese, Abror Khudoyberdiyev, Bennett Rennier, Anastasia Voloshinov. 2017-10-23. Classification of algebras of level two in the variety of nilpotent algebras and Leibniz algebras. https://doi.org/10.1016/j.geomphys.2018.08.012

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