Cup-Product for Leibniz Cohomology and Dual Leibniz Algebras

摘要

For any Lie algebra g there is a notion of Leibniz cohomology HL*(g), which is defined like the classical Lie cohomology, but with the nth tensor product g in place of the nth exterior product A~nQ. This Leibniz cohomology is defined on a larger class of algebras: the Leibniz algebras (cf. [LI], [L2]). A Leibniz algebra is a vector space equipped with a product satisfying a variation of the Jacobi identity: (1) [x,[y,z]]=[[x,y],z]-[[x,z],y].