Geodesic
Homology of Lie algebras with $\Lambda/q\Lambda$ coefficients and exact sequences
Theory and applications of categories, Tome 10 (2002), pp. 113-126 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

Classification : 18G10, 18G50.
Keywords: Lie algebra, nonabelian derived functor, exact sequence, homology group. 
@article{TAC_2002_10_a3,
     author = {Emzar Khmaladze},
     title = {Homology of {Lie} algebras with  $\Lambda/q\Lambda$ coefficients
and exact sequences},
     journal = {Theory and applications of categories},
     pages = {113--126},
     year = {2002},
     volume = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2002_10_a3/}
}
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and exact sequences
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Emzar Khmaladze. Homology of Lie algebras with  $\Lambda/q\Lambda$ coefficients
and exact sequences. Theory and applications of categories, Tome 10 (2002), pp. 113-126. http://geodesic.mathdoc.fr/item/TAC_2002_10_a3/