Contact and Frobenius solvable Lie algebras with abelian nilradical. Issue 10 (3rd October 2018)

• Record Type: Journal Article
• Authors: Alvarez, M. A.; Rodríguez-Vallarte, M. C.; Salgado, G.
• Is Part Of: Communications in algebra. Volume 46:Issue 10(2018)
• Page Start: 4344
• Page End: 4354
• Publication Date: 2018-10-03
• Subjects: Contact Lie algebras -- double extension of Lie algebras -- Frobenius Lie algebras -- Symplectic Lie algebras; Primary: 17Bxx -- Secondary: 53D10; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1439048
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: The aim of this work is to characterize the families of Frobenius (respectively, contact) solvable Lie algebras that satisfies the following condition: 𝔤 = 𝔥 ⋉ V, where 𝔥 ⊂ 𝔤𝔩 ( V ), | dim V − dim 𝔤 |≤1 and NilRad ( 𝔤 ) = V, V being a finite dimensional vector space. In particular, it is proved that every complex Frobenius solvable Lie algebra is decomposable, whereas that in the real case there are only two indecomposable Frobenius solvable Lie algebras.