Advanced Search

In this article, we provide an algorithm with Wolfram Mathematica code that gives a unified computational power in classification of finite dimensional nilpotent algebras using Skjelbred-Sund method. To illustrate the code, we obtain new finite dimensional Moufang algebras.

We connect the theorems of Rentschler [] and Dixmier [] on locally nilpotent derivations and automorphisms of the polynomial ring $A_0$ and of the Weyl algebra $A_1$, both over a field of characteristic zero, by establishing the same type of results for the family of algebras $$A_h=\langle x,y\mid yx-xy=h\left(x\right)\rangle ,$$ where $h$ is an arbitrary polynomial in $x$. In the second part of the paper we consider a field $𝔽$ of prime characteristic and study $𝔽\left[t\right]$comodule algebra structures on $A_h$. We also compute the Makar-Limanov invariant of absolute constants...