We study maximal Lie subalgebras among locally nilpotent derivations of the polynomial algebra. Freudenburg conjectured that the triangular Lie algebra of locally nilpotent derivations of the polynomial algebra is a maximal Lie algebra contained in the set of locally nilpotent derivations, and that every maximal Lie algebra contained in the set of locally nilpotent derivations is conjugate to the triangular Lie algebra. In this paper we prove the first part of the conjecture and present a counterexample to the second part. We also show that under a certain natural condition imposed on a maximal Lie algebra there is a conjugation taking this Lie algebra to the triangular Lie algebra.

Bibliography: 2 titles.

我们研究多项式代数的局部幂零导数中的最大李子代数。Freudenburg猜想多项式代数的局部幂零导数的三角李代数是局部幂零导数集合中包含的极大李代数，并且局部幂零导数集合中包含的每个极大李代数都与三角李代数共轭. 在本文中，我们证明了猜想的第一部分，并给出了第二部分的反例。我们还表明，在对最大李代数施加的特定自然条件下，存在将这个李代数与三角形李代数结合的共轭。

参考书目：2个标题。