Capelli type identities and enveloping algebras of Lie algebras

第一个结果是张量代数上导子的概念及其在非交换代数的不变量理论中的应用。G.张量代数或李代数的泛包络代数）。我还得到了这些结果的q-模拟。第二个结果是多项式代数和外代数的不变量理论的一系列第一和第二基本定理。我们有凯莱-汉密尔顿型定理背后的这些第二基本定理。此外，这些外代数的第二基本定理与多项式恒等式理论密切相关。

The first result is the notion of derivations on tensor algebras and its applications to the invariant theory of noncommutative algebras(e. g. tensor algebras or universal enveloping algebras of Lie algebras). I also obtained a q-analogue of these results. The second result is some series of first and second fundamental theorems of invariant theory for polynomial algebras and exterior algebras. We have Cayley-Hamilton type theorems behind these second fundamental theorems. In addition, these second fundamental theorems for exterior algebras are closely related to the theory of polynomial identities.