# Structure of locally conformally symplectic Lie algebras and solvmanifolds

## TL;DR

This paper classifies locally conformally symplectic structures on four-dimensional Lie algebras and constructs such structures on compact quotients of all four-dimensional solvable Lie groups, advancing understanding of these geometric structures.

## Contribution

It provides a complete classification of locally conformally symplectic structures on four-dimensional Lie algebras and constructs examples on compact solvmanifolds, filling gaps in the geometric theory.

## Key findings

- Classification of structures on all four-dimensional Lie algebras
- Construction of structures on compact quotients of solvable Lie groups
- Extension of locally conformally symplectic geometry to new classes of manifolds

## Abstract

We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients of all four-dimensional connected and simply connected solvable Lie groups.