Left-symmetric algebra structures on contact Lie algebras

Abstract

The aim of this work is to give necessary and sufficient conditions to extend an LSA structure on a Lie algebra $\mathfrak{h}$ to a Lie algebra $\mathfrak{g}$ that either contains $\mathfrak{h}$ 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.

Mathematics Subject Classification:

• Primary: 17Bxx, 17D25
• Secondary: 53Dxx

Keywords:

• Contact Lie algebras
• Frobenius Lie algebra
• left-symmetric algebra structure

Additional information

Funding

The authors would like to acknowledge the support received by PRODEP grant UASLP-CA-228 and CONACyT Grant: A1-S-45886.