Cohomology ring of -Lie algebras

Abstract

Natural graded Lie brackets on the space of cochains of -Leibniz and -Lie algebras are introduced. It turns out that these brackets agree under the natural embedding introduced by Gautheron. Moreover, -Leibniz and -Lie algebras turn to be canonical structures for these brackets in a similar way in which associative algebras (respectively, Lie algebras) are canonical structures for the Gerstenhaber bracket (respectively, Nijenhuis-Richardson bracket). This allows to define the corresponding cohomology operators and graded Lie algebra structures on the cohomology spaces in an uniform simple way by means of square zero elements.peerReviewe