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首页> 外文期刊>Siberian Mathematical Journal >Enumeration of maximal subalgebras in free restricted lie algebras
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Enumeration of maximal subalgebras in free restricted lie algebras

机译：自由受限李代数中最大子代数的枚举

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Given a finitely generated restricted Lie algebra L over the finite field , and n ≥ 0, denote by a n (L) the number of restricted subalgebras H ? L with L/H = n. Denote by ? n (L) the number of the subalgebras satisfying the maximality condition as well. Considering the free restricted Lie algebra L = F d of rank d ≥ 2, we find the asymptotics of ? n (F d ) and show that it coincides with the asymptotics of a n (F d ) which was found previously by the first author. Our approach is based on studying the actions of restricted algebras by derivations on the truncated polynomial rings. We establish that the maximal subalgebras correspond to the so-called primitive actions. This means that “almost all” restricted subalgebras H ? F d of finite codimension are maximal, which is analogous to the corresponding results for free groups and free associative algebras.
机译：给定有限域上有限生成的受限李代数L，且n≥0，则用n（L）表示受限子代数H？ L / H = n的L。用？表示n（L）满足最大条件的子代数的个数考虑等级d≥2的自由受限李代数L = F d，我们找到的渐近性。 n（F d）并显示出它与第一作者先前发现的n（F d）的渐近性一致。我们的方法基于通过对截断的多项式环求导来研究受限代数的作用。我们确定最大子代数对应于所谓的原始动作。这意味着“几乎所有”受限子代数H？有限维的F d最大值，类似于自由群和自由缔合代数的相应结果。

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