COTRIPLE HOMOLOGY OF CROSSED 2-CUBES OF LIE ALGEBRAS

The cotriple homology of crossed 2-cubes of Lie algebras is constructed and investigated. Namely, we calculate the cotriple homology of an inclusion crossed 2-cube of Lie algebras in terms of the bi-relative Chevalley–Eilenberg homologies. We also define in a natural way the Chevalley–Eilenberg homology of crossed 2-cubes of Lie algebras and study the relationship between cotriple and Chevalley–Eilenberg homologies for any crossed 2-cube of Lie algebras. We show that low-dimensional cyclic homologies of associative algebras are calculated in terms of the cotriple homology of crossed 2-cubes of Lie algebras.