Double extensions of left-symmetric structures

Abstract

The notion of double extension for symplectic Lie algebras was introduced by Medina and Revoy in 1985. In 2021, Valencia gave a condition for symplectic Lie algebras which are obtained through double extension to admit compatible left-symmetric structures. In this paper, we formulate the notion of double extension for left-symmetric structures and give a condition for left-symmetric structures to be obtained through double extension. Moreover, we prove that right nilpotent left-symmetric structures on some solvable Lie algebras are obtained through double extension. We also give a condition for left-symmetric structures which are obtained through double extension to be complete.

Keywords:

• Double extension
• double extension of left-symmetric structures
• trivial left-symmetric structure

2020 Mathematics Subject Classification:

• 17A30
• 17B60
• 53B05

Disclosure statement

The author reports there are no competing interests to declare.

Additional information

Funding

This work was supported by JSPS KAKENHI under Grant Number JP18K13418.