Semi-invariants of low-dimensional Lie algebras

Abstract

Abstract The aim of this work is to explicitly compute the semi-invariants of low-dimensional Lie algebras by reducing the amount of work, i.e., we can prove that almost every irreducible Lie algebra of dimension less than or equal to 5, satisfies the following: It is either a contact Lie algebra or there exists a torus such that is a contact Lie algebra. Therefore, the semi-invariants found by using the contact structure are the same found by using the Frobenius structure.