Leibniz Homology Research Articles

On the Leibniz Homology of Poisson Algebras

We study the Leibniz homology of the Poisson algebra of polynomial functions over (ℝ2n,ω) where ω is the standard symplectic structure. We identify it with certain highest-weight vectors of some \(\mathfrak{s}\mathfrak{p}\)2n(\(\mathbb{C}\))-modules and obtain some explicit result in low degree.

Homologie des algèbres stables de matrices sur une A∞-algèbre

We prove that the algebra of matrices over an A ∞ -algebra A can be endowed with a structure of Leibniz algebra up to homotopy. The main theorem of this Note states that the Leibniz homology of the stable algebra of matrices over A can be expressed in terms of the Hochschild homology of A. This theorem extends the result of Cuvier and Loday proved in the framework of associative algebras.

Leibniz homology of unitary Lie algebras

Leibniz homology of unitary Lie algebras

Leibniz homilogy of dialgebras of matrices

A dialgebra D is a vector space with two associative operations ÷, ⊢ satisfying three more relations. By setting [ x, y] : = x ÷ y − y ⊢ x, any dialgebra gives rise to a Leibniz algebra. Here we compute the Leibniz homology of the dialgebra of matrices gl( D) with entries in a given dialgebra D. We show that HL( gl( D)) is isomorphic to the tensor module over HHS( D), which is a variation of the natural dialgebra homology HHY( D).

Leibniz Homology of Extended Lie Algebras

Leibniz Homology of Extended Lie Algebras

Suite spectrale d'une extension d'algèbres de Leibniz

Leibniz homology is a non-commutative homology theory for Lie algebras which can be extended to a larger class of algebras: the Leibniz algebras. We construct a “Leibniz version” of the Hochschild-Serre spectral sequence.

Leibniz homology and the Hilton-Milnor theorem

Leibniz homology and the Hilton-Milnor theorem

Leibniz Homology and the James Model

Leibniz Homology and the James Model