论文标题
修改后的Makar-Limanov和Derksen不变
Modified Makar-Limanov and Derksen invariants
论文作者
论文摘要
我们研究了仿射代数品种的修改后的Makar-Limanov和Derksen不变性。修改后的Makar-Limanov不变性是所有局部nilpotent衍生物与切片的核的相交，而修改后的derkesen不变性是这些核产生的子algebra。我们证明，如果存在与切片的局部尼尔氏派生，则修改了Makar-Limanov与Makar-Limanov不变的不变。另外，我们构建了一个示例的示例，该示例是用切片纳入本地nilpotent派生的示例，使得修改的德克森不变式与德克森不变不变不一致。
We investigate modified Makar-Limanov and Derksen invariants of an affine algebraic variety. The modified Makar-Limanov invariant is the intersection of kernels of all locally nilpotent derivations with slices and the modified Derksen invariant is the subalgebra generated by these kernels. We prove that modified Makar-Limanov invariant coincide with Makar-Limanov invariant if there exists a locally nilpotent derivation with a slice. Also we construct an example of a variety admitting a locally nilpotent derivation with a slice such that modified Derksen invariant does not coincide with Derksen invariant.
