English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let $K$ be an algebraically closed field of characteristic zero, $A =K[x_1,\dots,x_n]$ the polynomial ring, $R = K(x_1,\dots,x_n)$ the field ofrational functions, and let $W_n(K) = \Der_{K}A$ be the Lie algebra of all$K$-derivations on $A$. If $D \in W_n(K),$ $D\not =0$ is linear (i.e. of theform $D = \sum_{i,j=1}^n a_{ij}x_j \frac{\partial}{\partial x_i}$) we give adescription of the centralizer of $D$ in $W_n(K)$ and point out an algorithmfor finding generators of $C_{W_n(K)}(D)$ as a module over the ring ofconstants in case when $D$ is the basic Weitzenboeck derivation. In moregeneral case when the ring $A$ is a finitely generated domain over $K$ and $D$is a locally nilpotent derivation on $A,$ we prove that the centralizer$C_{{\rm Der}A}(D)$ is a "large" \ subalgebra in ${\rm Der}_{K} A$, namely$\rk_A C_{\Der A}(D) := \dim_R RC_{\Der A}(D)$ equals ${\rm tr}.\deg_{K}R,$where $R$ is the field of fraction of the ring $A.

Centralizers of linear and locally nilpotent derivations