#
Homology of Lie algebras with $\Lambda/q\Lambda$ coefficients
and exact sequences

##
Emzar Khmaladze

Using the long exact sequence of nonabelian derived functors, an
eight term exact sequence of Lie algebra homology with $\Lambda/q\Lambda$
coefficients is obtained, where $\Lambda$ is a ground ring and $q$ is
a nonnegative integer. Hopf formulas for the second and third
homology of a Lie algebra are proved. The condition for the
existence and the description of the universal $q$-central
relative extension of a Lie epimorphism in terms of relative
homologies are given.

Keywords: Lie algebra, nonabelian derived functor, exact sequence, homology group.

2000 MSC: 18G10, 18G50.

*Theory and Applications of Categories*, Vol. 10, 2002, No. 4, pp 113-126.

http://www.tac.mta.ca/tac/volumes/10/4/10-04.dvi

http://www.tac.mta.ca/tac/volumes/10/4/10-04.ps

http://www.tac.mta.ca/tac/volumes/10/4/10-04.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/4/10-04.dvi

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