Rank and rigidity of locally nilpotent derivations of affine fibrations

Locally nilpotent derivations on $\mathbb{A}^2$-fibrations with $\mathbb{A}^1$-fibration kernels

In this paper, we give a characterization of locally nilpotent derivations on $\mathbb{A}^2$-fibrations over Noetherian domains containing $\mathbb{Q}$ having kernel isomorphic to an $\mathbb{A}^1$-fibration.

Structure of $\mathbb{A}^2$-fibrations Having Fixed Point Free Locally Nilpotent Derivations

In this article, we show that a fixed point free locally nilpotent derivation of an $\mathbb{A}^2$-fibration over a Noetherian ring containing $\mathbb{Q}$ has slice.

On the rigidity of certain Pham-Brieskorn rings

Fix a field $k$ of characteristic zero. If $a_1, ..., a_n$ ($n>2$) are positive integers, the integral domain $B = k[X_1, ..., X_n] / ( X_1^{a_1} + ... + X_n^{a_n} )$ is called a Pham-Brieskorn ring. It is conjectured that if $a_i > 1$ for all $i$ and $a_i=2$ for at most one $i$, then $B$ is rigid. (A ring $B$ is said to be rigid if the only locally nilpotent derivation $D: B \to B$ is the zero derivation.) We give partial results towards the conjecture.

分次整环及其Veronese子环的刚性

Rigidity of Graded Integral Domains and of their Veronese Subrings

研究分次整环的刚性是否遗传给其Veronese子环，以及子环的导子能否扩展到原环，刻画使Veronese子环非刚性的子群性质。

局部有限导子李代数的刚性

Rigidity for Lie algebras of locally finite derivations

该研究证明特征零域上有限生成交换代数的局部有限导子生成的有限生成李子代数必有限维，解决了Popov2005年关于幂单单参数子群的问题，还刻画了多项式控制系统的双线性实现。