Cosymplectic and $\alpha$-cosymplectic Lie algebras

Abstract

We completely characterize cosymplectic and $\alpha$-cosymplectic Lie algebras in terms of corresponding symplectic Lie algebras and suitable derivations on them. Several examples are given and classification results are obtained in dimension five for cosymplectic, $K$-cosymplectic and coK\"ahler Lie algebras.