Classification of three-dimensional Lie algebras in \(\mathbb{R}^3\) and their second-order differential invariants
In this paper some results from the author's unpublished dissertation (1991) are listed. On the basis of the well known classification of three-dimensional real Lie algebras a classification (23 types) up to similarity of three-dimensional algebras of the first order differential operators on \( \mathbb R^3\) (or, that is equivalent, of three-dimensional Lie algebras of vector fields -- it is not specified, smooth or analytic -- on \(\mathbb R^3\)) is given. Let's notice that this classification may be extracted from works of S. Lie. The new result of the article is a list of differential invariants of the second order as functions of two variables for all specified Lie algebras of differential operators. A proof of this result in the article is absent.
scientific article; zbMATH DE number 6115123