Classification of differentially non-degenerate left-symmetric algebras in dimension 3

Abstract

In terms of Nijenhuis geometry, left-symmetric algebras are the same as Nijenhuis operators whose entries are linear in coordinates. Here we consider Nijenhuis operators for which the coefficients of its characteristic polynomial are algebraically independent. We give a classification of this type of operators and hence of the corresponding LSAs (which we will call differentially non-degenerate LSA) in dimension 3.