SOME PROPERTIES ON THE TENSOR SQUARE OF LIE ALGEBRAS

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/L-2 of finite dimension, we prove L circle times L congruent to L square L circle times L Lambda L and Z(Lambda) (L) boolean AND L-2 = Z(circle times)(L). Moreover, we show that L Lambda L is isomorphic to derived subalgebra of a cover of L, and finally we give a free presentation for it.