秩>= 1的幂零李代数的Grunewald-O 'Halloran猜想
The Grunewald-O'Halloran conjecture for nilpotent Lie algebras of rank >= 1
摘要：
Grunewald和O 'Halloran在1993年证明了每一个复幂零李代数都是另一个非同构李代数的退化。证明了关于允许半单导子的幂零李代数类的猜想，对于特征幂零李代数类仍是开放的。在第一个特征幂零李代数出现的7维空间中，证明了猜想，并证明了每个7维幂零李代数的非平凡退化。
英文摘要：
Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, non isomorphic, Lie algebra. We prove the conjecture for the class of nilpotent Lie algebras admitting a semisimple derivation, remaining open for the class of characteristically nilpotent Lie algebras. In dimension 7, where the first characteristically nilpotent Lie algebras appear, we prove the conjecture and we also exhibit explicit nontrivial degenerations to every 7-dimensional nilpotent Lie algebra.
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