Let L be a non-abelian restricted Lie algebra over a field of characteristic p > 0 and let u(L) denote its restricted enveloping algebra. In Siciliano (Publ Math (Debr) 68:503–513, 2006) it was proved that if u(L) is Lie solvable then the Lie derived length of u(L) is at least ⌈log2(p + 1)⌉. In the present paper we characterize the restricted enveloping algebras whose Lie derived length coincides with this lower bound.
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机译:设L为特征p> 0的场上的非阿贝尔受限李代数,设u(L)表示其受限包络代数。在西西利亚诺(Publ Math(Debr)68:503–513,2006)中,证明了如果u(L)是李可解的,那么u(L)的Lie衍生长度至少为⌈log 2 sub >(p + 1)⌉。在本文中,我们描述了其Lie导出长度与此下界一致的受限包络代数。
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