Related papers: On Leibniz cohomology
Hochschild (co)homology and Pirashvili's higher order Hochschild (co)homology are useful tools for a variety of applications including deformations of algebras. When working with higher order Hochschild (co)homology, we can consider the…
In this paper we use invariant theory to develop the notion of cohomological detection for Type I classical Lie superalgebras. In particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller…
By elementary and direct calculations the vanishing of the (algebraic) second Lie algebra cohomology of the Witt and the Virasoro algebra with values in the adjoint module is shown. This yields infinitesimal and formal rigidity or these…
In this paper, we study the cup products and Betti numbers over cohomology superspaces of two-step nilpotent Lie superalgebras with coefficients in the adjoint modules over an algebraically closed field of characteristic zero. As an…
We compute the Hochschild cohomology of Hilbert schemes of points on surfaces and observe that it is, in general, not determined solely by the Hochschild cohomology of the surface, but by its "Hochschild-Serre cohomology": the bigraded…
We prove that the homology groups of any connected reductive group over a field with coefficients in the Steinberg representation vanish in a range. The generalizes work of Ash-Putman-Sam on the classical split groups. We state a…
Bakalov, Kac and Voronov introduced Leibniz conformal algebras (and their cohomology) as a non-commutative analogue of Lie conformal algebras. Leibniz conformal algebras are closely related to field algebras which are non-skew-symmetric…
For a field $\mathbb{F}$, let $L_k(\mathbb{F})$ be the Lie algebra of derivations $f(t)\frac{d}{dt}$ of the polynomial ring $\mathbb{F}[t]$, where $f(t)$ is a polynomial of degree $\geqslant k$. For any $k\geqslant -1$, we present a basis…
The Gerstenhaber and Schack cohomology comparison theorem asserts that there is a cochain equivalence between the Hochschild complex of a certain algebra and the usual singular cochain complex of a space. We show that this comparison…
We introduce the enveloping algebra for a Leibniz pair, and show that the category of modules over a Leibniz pair is isomorphic to the category of left modules over its enveloping algebra. Consequently, we show that the cohomology theory…
In this paper we determine the first Hochschild homology and cohomology with different coefficients for gentle algebras and we give a geometrical interpretation of these (co)homologies using the ribbon graph of a gentle algebra as defined…
The purpose of this paper is to study global deformations of Hom-Leibniz algebras. We introduce a cohomology for Hom-Leibniz algebras with values in a Hom-module, characterize versal deformations and provide examples.
The space of Lie algebra cohomology is usually described by the dimensions of components of certain degree even for the adjoint module as coefficients when the spaces of cochains and cohomology can be endowed with a Lie superalgebra…
We use a Mayer-Vietoris-like spectral sequence to establish vanishing results for the cohomology of complements of linear and elliptic hyperplane arrangements, as part of a more general framework involving duality and abelian duality…
We introduce the notion of c-nilpotent Schur Lie-multiplier of Leibniz algebras. We obtain exact sequences and formulas of the dimensions of the underlying vector spaces relating the c-nilpotent Schur Lie-multiplier of a Leibniz algebra Q…
In this article, we first consider the $L^{2}$ \textit{Morse-Novikov cohomology} on a complete Riemannian manifold $M$ equipped with a parallel $1$-form which includes Vaisman manifold. Based on a vanishing theorem of $L^{2}$…
This note presents a general theorem about the cohomology of finite dimensional Lie algebras of arbitrary characteristic. As an application we compute the cohomology of the Borel subalgebra of sl(N).
A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…
We interpret Hochschild cohomology as the Lie algebra of the derived Picard group (in the sense of Rouquier-Zimmermann and Yekutieli) and deduce that it is preserved under derived equivalences.
This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear…