The problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.

中文翻译：

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构造性非交换不变理论

在一组有限维李代数的自同构对其通用包络代数的作用下寻找不变子代数的生成器的问题被简化为寻找作用在李代数的对称张量代数上的同一组的齐次生成器。此过程适用于证明Lie幂等相对自由的关联代数中的不变量代数的构造性Hilbert-Nagata定理（包括度界），该代数具有归因于还原族表示的作用。