Eight-dimensional symplectic non-solvable Lie algebras

Abstract

In this paper, we classify eight-dimensional non-solvable Lie algebras that support a symplectic structure. As well as a complete classification is given, up to symplectomorphism, of eight-dimensional symplectic non-solvable Lie algebras.

KEYWORDS:

• Frobenius algebras
• left-symmetric algebras
• Levi decomposition
• symplectic Lie algebras

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B30
• 17B60
• 53D05

Acknowledgments

The authors wish to thank S. El bourkadi for having read carefully the first version of the paper and pointing out many typing and style mistakes.