Semi-invariants of low-dimensional Lie algebras. Issue 5 (4th May 2021)

• Record Type: Journal Article
• Authors: Alvarez, M. A.; Salgado, G.
• Is Part Of: Communications in algebra. Volume 49:Issue 5(2021)
• Page Start: 2022
• Page End: 2032
• Publication Date: 2021-05-04
• Subjects: Contact Lie algebras -- Frobenius Lie algebras -- invariants -- semi-invariants; Primary: 17Bxx -- Secondary: 53D10; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1861619
• Languages: English
• ISSNs: 0092-7872

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 g, of dimension less than or equal to 5, satisfies the following: It is either a contact Lie algebra or there exists a torus T ⊂ Der ( g ) such that T ⋉ g is a contact Lie algebra. Therefore, the semi-invariants found by using the contact structure are the same found by using the Frobenius structure.