Homology of Lie algebras with \(\Lambda/q\Lambda\) coefficients and exact sequences (Q2768443)

\(\Lambda\) is a commutative ring and \(q\) is a nonnegative integer. The paper studies first derived functors of the nonabelian exterior square modulo \(q\) of a \(\Lambda\)-Lie algebra. Relation with homology groups is established.NEWLINENEWLINENEWLINEThe long exact sequence of derived functors leads to an eight terms exact sequence of Lie algebra homology with \(\Lambda/q \Lambda\) coefficients.NEWLINENEWLINENEWLINEAs an application, the mod \(q\) versions of Hopf formulas for the second and third homologies are proved. The existence and description (in terms of relative homologies) of the universal \(q\)-central relative extension for a Lie epimorphism is the last result.