Cup-product for Leibniz Cohomology and Dual Leibniz Algebras
نویسنده
چکیده
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 n-th tensor product g⊗n in place of the n-th exterior product Λ g. This Leibniz cohomology is defined on a larger class of algebras : the Leibniz algebras (cf. [L1], [L2]). A Leibniz algebra is a vector space equipped with a product satisfying a variation of the Jacobi identity :
منابع مشابه
Some remarks about the second Leibniz cohomology group for Lie algebras
We compare by a very elementary approach the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones. Examples are given of coupled cocycles. Some properties are deduced as to Leibniz deformations. We also consider the class of Lie algebras for which the Koszul 3-form is zero, and prove that it contains all quotients of Borel subalgebras, or of their nilradicals,...
متن کاملForum Mathematicum Leibniz N-algebras
A Leibniz n-algebra is a vector space equipped with an n-ary operation which has the property of being a derivation for itself. This property is crucial in Nambu mechanics. For n 2 this is the notion of Leibniz algebra. In this paper we prove that the free Leibniz n 1algebra can be described in terms of the n-magma, that is the set of n-ary planar trees. Then it is shown that the n-tensor ...
متن کاملUniversal enveloping algebras of Leibniz algebras and (co)homology
The homology of Lie algebras is closely related to the cyclic homology of associative algebras [LQ]. In [L] the first author constructed a "noncommutative" analog of Lie algebra homology which is, similarly, related to Hochschild homology [C, L]. For a Lie algebra g this new theory is the homology of the complex C,(g) ... ~ ~| g|-+ ... ~1 ~ k, whose boundary map d is given by the formula d(gl|1...
متن کاملDeformation of Dual Leibniz Algebra Morphisms
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
متن کامل