On some connected groups of automorphisms of Weil algebras

TL;DR

This paper details a method for directly calculating the automorphism groups of Weil algebras, focusing on cases where the automorphism group is connected and analyzing specific determinant conditions.

Contribution

It introduces a detailed calculation method for automorphism groups of Weil algebras, especially for connected groups with particular determinant properties.

Findings

Explicit calculation method for automorphism groups of Weil algebras

Analysis of cases with specific determinant values

Focus on connected automorphism groups

Abstract

The method of direct calculation of the group of $\mathbb R$-algebra automorphisms of a Weil algebra is presented in detail. The paper is focused on the case of a one-componental group and presents two cases of values of the determinant of its linear part.