Geodesic
Homology of Lie algebras with $\Lambda/q\Lambda$ coefficients and exact sequences
Theory and applications of categories, Tome 10 (2002), pp. 113-126

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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
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     journal = {Theory and applications of categories},
     pages = {113--126},
     publisher = {mathdoc},
     volume = {10},
     year = {2002},
     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/