A note on multidegrees of automorphisms of the form \((\exp D)_{\star}\)

• Date: 2023
• Main Authors: Karaś, M., Pękała, P.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: derivation; locally nilpotent derivation; polynomial automorphism; multidegree; 13N15; 14R10; 16W20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2042
• Journal Title: Algebra and Discrete Mathematics

Let \(k\) be a field of characteristic zero. For any polynomial mapping \(F=(F_1,\ldots,F_n):k^n\rightarrow k^n\) by multidegree of \(F\) we mean the following \(n\)-tuple of natural numbers mdeg \(F=(\deg F_1,\ldots,\deg F_n).\) Let us denote by \(k[x]=k[x_1,\ldots,x_n]\) a ring of polynomials in \...