Rational equivalence for enveloping algebras of three-dimensional Lie algebras

TL;DR

This paper investigates the rational equivalence of enveloping algebras associated with three-dimensional Lie algebras, focusing on those with a two-dimensional derived subalgebra over algebraically closed fields of any characteristic.

Contribution

It provides a detailed analysis of the rational equivalence classes of these enveloping algebras, extending understanding across different characteristics.

Findings

Classification of rational equivalence classes for these enveloping algebras

Results applicable to fields of arbitrary characteristic

Enhanced understanding of the structure of enveloping algebras in low dimensions

Abstract

We study from the point of view of rational equivalence the enveloping algebras of Lie algebras of dimension 3 whose derived Lie subalgebra is of dimension 2, over an algebraically closed base field in arbitrary characteristics.