Xiankun Du

activity

20112022

most citedPolynomial maps with invertible sums of Jacobian matrices and of directional Derivatives

4 citations · 10 across the 8 of their papers we have counts for

collaborators

8 papers

math.RA2022

Set-theoretical solutions to the Hom-Yang-Baxter equation and Hom-cycle sets

Kaiqiang Zhang, Xiankun Du

Set-theoretic solutions to the Yang-Baxter equation have been studied extensively by means of related algebraic systems such as cycle sets and braces, dynamical versions of which h…

math.AC2022

Images of locally finite $E$ -derivations of bivariate polynomial algebras

Hongyu Jia, Xiankun Du, Haifeng Tian

This paper presents an $E$ -derivation analogue of a result on derivations due to van den Essen, Wright and Zhao. We prove that the image of a locally finite $K$ -$\mathcal…

math.AC2021

Images of Linear Derivations and Linear E-derivations of K[x 1 ,x 2 ,x 3 ]

Haifeng Tian, Xiankun Du, Hongyu Jia

Let K be a field of characteristic zero. We prove that images of a linear K-derivation and a linear K-E-derivation of the ring K[x 1 ,x 2 ,x 3 ] of polynomial in three variables ov…

math.RA2018

Adjoint cohomology of two-step nilpotent Lie superalgebras

Wende Liu, Yong Yang, Xiankun Du

In this paper, we study the cup products and Betti numbers over cohomology superspaces of two-step nilpotent Lie superalgebras with coefficients in the adjoint modules over an alge…

math.RA2013★ 1 cited

Representations for the Drazin inverse of the generalized Schur complement

Daochang Zhang, Xiankun Du

In this paper we present expressions for the Drazin inverse of the generalized Schur complement $A - C D^{d} B$ in terms of the Drazin inverses of $A$ and the generalized Schur complem…

math.AC2012★ 2 cited

Multidegrees of Tame automorphisms with one prime number

Jiantao Li, Xiankun Du

Let $3 \leq d_{1} \leq d_{2} \leq d_{3}$ be integers. We show the following results: (1) If $d_{2}$ is a prime number and $\frac{d _{1}}{g c d ( d _{1} , d _{3} )} \neq = 2$ , then $(d_{1}, d_{2}, d_{3})$ is a multidegr…

math.AC2011★ 3 cited

Tame automorphisms with multidegrees in the form of arithmetic progressions

Jiantao Li, Xiankun Du

Let $(a, a + d, a + 2 d)$ be an arithmetic progression of positive integers. The following statements are proved: (1) If $a ∣ 2 d$ , then $(a, a+d, a+2d)\in\mdeg(\Tame(\mathbb{C}^3))$. (2…

math.AC2011★ 4 cited

Polynomial maps with invertible sums of Jacobian matrices and of directional Derivatives

Hongbo Guo, Michiel de Bondt, Xiankun Du +1

Let $F : C^{n} \to C^{m}$ be a polynomial map with $d e g F = d \geq 2$ . We prove that $F$ is invertible if $m = n$ and $\sum_{i = 1}^{d - 1} J F (α_{i})$ is invertible for all $i$ , which is…