Grunewald–O'Halloran conjecture for nilpotent Leibniz algebras

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Let AA be an nn-dimensional nilpotent Leibniz algebra with n≥2n\ge 2. A degeneration B→AB\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 n≥2n\ge 2, there exists an nn-dimensional non-nilpotent Leibniz algebra BB such that B→AB\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.

References

Primary source

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

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