Principal derivations and codimension one ideals in contact and Frobenius Lie algebras. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Barajas, T.; Roque, E.; Salgado, G.
• Is Part Of: Communications in algebra. Volume 47:Issue 12(2019)
• Page Start: 5380
• Page End: 5391
• Publication Date: 2019-12-02
• Subjects: Contact Lie algebras -- symplectic Lie algebras -- Frobenius Lie algebras -- principal element -- principal derivations; Primary: 17B05, 17B99 -- Secondary: 53D10, 17B81; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1623238
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: The aim of this work is twofold. First, we give an inductive procedure to construct a Frobenius (resp. contact) Lie algebra from a contact (resp. Frobenius) Lie algebra. Second, we prove that all Frobenius Lie algebras can be constructed in this way, i.e., every Frobenius Lie algebra can be constructed as an extension of a contact Lie algebra by adding a distinguished element called principal derivation . Hence, classification of Frobenius Lie algebras will follow from classification of contact Lie algebras and every contact Lie algebra which admits a principal derivation is isomorphic to a subalgebra of s l m . As an example, we classify all 4-dimensional Frobenius Lie algebra.