### Non-abelian (co)homology of Lie algebras, by Nick Inassaridze, Emzar Khmaladze, and Manuel Ladra

Non-abelian homology of Lie algebras with coefficients in Lie algebras is constructed and
studied, generalising the classical Chevalley-Eilenberg homology of Lie algebras.
The relation of cyclic homology with Milnor cyclic homology of non-commutative associative
algebras is established in terms of the long exact non-abelian homology sequence of Lie
algebras. Some explicit formulas for the second and the third non-abelian homology of
Lie algebras are obtained. Using the generalised notion of the Lie algebra of derivations,
we introduce the second non-abelian cohomology of Lie algebras with coefficients in crossed
modules and extend the seven-term exact non-abelian cohomology sequence of Guin to
nine-term exact sequence.

Nick Inassaridze <inas@rmi.acnet.ge>

Emzar Khmaladze <khmal@rmi.acnet.ge>

Manuel Ladra <ladra@usc.es>