Abstract

In the present paper we extend the results of [2, 4] for the tensor square of Lie algebras. More precisely, for any Lie algebra L with L/L² of finite dimension, we prove L ⊗ L ≅ L □ L ⊕ L ∧ L and Z^∧(L) ∩ L² = Z^⊗(L). Moreover, we show that L ∧ L is isomorphic to derived subalgebra of a cover of L, and finally we give a free presentation for it.