Grunewald–O'Halloran conjecture for nilpotent Leibniz algebras

Let AA be an nn-dimensional nilpotent Leibniz algebra with n2n\ge 2. A degeneration BAB\to A means that the nn-dimensional non-nilpotent Leibniz algebra BB degenerates to AA. Grunewald–O'Halloran conjecture. For any nn-dimensional nilpotent Leibniz algebra AA with n2n\ge 2, there exists an nn-dimensional non-nilpotent Leibniz algebra BB such that BAB\to A. This is the Leibniz-algebra analogue of the Grunewald–O'Halloran conjecture for Lie algebras; the source mentions partial results in related algebra varieties but gives no resolution of this general assertion.

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Primary source

Nurlan Ismailov, Ivan Kaygorodov and Yury Volkov, “The geometric classification of Leibniz algebras”, arXiv:1705.04346 (2021).

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