Homology with Trivial Coefficients and Universal Central Extensions of Algebras with Bracket

A 5-term exact sequence and the interpretation of low dimensional groups of homology with trivial coefficients of algebras with bracket are obtained. The endofunctor in the category of algebras with bracket which assigns to a perfect algebra with bracket its universal central extension is constructed and the characterization of the universal central extension by means of the low-dimensional homology groups is done. The conditions required to lift an automorphism or a derivation of A to A′ in a covering f:A′ ? A are analyzed.