论文标题
局部nilpotent衍生的最大谎言子代数
Maximal Lie subalgebras of locally nilpotent derivations
论文作者
论文摘要
基因弗洛伊堡（Gene Freudenburg）猜想，对于多项式环，三角形谎言代数是最大的谎言代数，位于环的局部nilpotent派生中。还猜想，彼此之间的最大谎言代数位于多项式环的局部nilpotent衍生物集中，将其连接到三角形谎言代数。在目前的工作中，我们证明了该猜想的第一部分，并为第二部分提供了反例。我们还表明，猜想的第二部分是局部nilpotent派生中最大代数的最大代数，具有一些自然的其他特性。
It has been conjectured by Gene Freudenburg that for a polynomial ring, the triangular Lie algebra is the maximal Lie algebra which lies in the set of locally nilpotent derivations of the ring. Also it was conjectured that each other maximal Lie algebra which lies in the set of locally nilpotent derivations of the polynomial ring is conjugated to the triangular Lie algebra. In the present work we prove the first part of this conjecture and provide the counterexample to the second part. Also we show that the second part of the conjecture holds for the maximal Lie algebras among locally nilpotent derivations with some natural additional properties.
