Grunewald–O'Halloran conjecture for nilpotent Leibniz algebras
Grunewald–O'Halloran conjecture for nilpotent Leibniz algebras
Let be an -dimensional nilpotent Leibniz algebra with . A degeneration means that the -dimensional non-nilpotent Leibniz algebra degenerates to . Grunewald–O'Halloran conjecture. For any -dimensional nilpotent Leibniz algebra with , there exists an -dimensional non-nilpotent Leibniz algebra such that . 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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