Left-symmetric algebra structures on contact Lie algebras. Issue 7 (3rd July 2023)

• Record Type: Journal Article
• Authors: Méndez-Méndez, F. O.; Salgado, G.
• Is Part Of: Communications in algebra. Volume 51:Issue 7(2023)
• Page Start: 2914
• Page End: 2929
• Publication Date: 2023-07-03
• Subjects: Primary: 17Bxx, 17D25 -- Secondary: 53Dxx; Contact Lie algebras -- Frobenius Lie algebra -- left-symmetric algebra structure; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2023.2173767
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: The aim of this work is to give necessary and sufficient conditions to extend an LSA structure on a Lie algebra h to a Lie algebra g that either contains h as a subalgebra, or is a central extension of it. We also study conditions under which a Lie algebra together with an LSA structure admit a Frobenius or a contact form. Furthermore, we describe the properties of the Reeb vector associated with the codimension one contact ideal with respect to the LSA structure on the Frobenius Lie algebra.