Related papers: Derived intersections and free dg-Lie algebroids
We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra…
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differential Lie algebras of weight 1 when the action is the adjoint…
We introduce twist left-veering mapping classes of punctured surfaces. We prove that a twist left-veering open book supports an overtwisted contact structure and determine when the closed braid coming from the punctures is loose or…
In this paper, we present some basic properties concerning the derivation algebra ${\rm Der}(T)$, the quasiderivation algebra ${\rm QDer}(T)$ and the generalized derivation algebra ${\rm GDer}(T)$ of a Lie triple system $T$, with the…
Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support {\tau}-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given…
This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…
In this paper, we give a purely cohomological interpretation of the extension problem for (super) Lie algebras; that is the problem of extending a Lie algebra by another Lie algebra. We then give a similar interpretation of infinitesimal…
One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative…
This paper studies how the theory of derived algebras (in the sense of Bhatt-Mathew and Raksit) interacts with formal derived geometry, specifically the formal derived stacks which show up in the theory of prismatization. As an application…
The twist deformations for simple Lie algebras U(g) whose twisting elements F are known explicitly are usually defined on the carrier subspace injected in the Borel subalgebra B^+(g). We solve the problem of creating the parabolic twist F_P…
In present work, we find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix…
In this note we motivate the definition and use of Lie algebroids by revisiting the problem of reconstructing a hypersurface in Euclidean space from infinitesimal data.
Let $\mathfrak{g}$ be a Color Lie Algebra and $\mathcal{U}(\mathfrak{g})$ its the universal Enveloping Algebra. We define the notion of graded deformations and we give explicit graded deformations of the universal Enveloping Algebra of…
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…
We develop the theory of truncated wedge schemes, a higher dimensional analog of jet schemes. We prove some basic properties and give an irreducibility criterion for truncated wedge schemes of a locally complete intersection variety…
One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial…
Given a transitive DG-Lie algebroid $(\mathcal{A}, \rho)$ over a smooth separated scheme $X$ of finite type over a field $\mathbb{K}$ of characteristic $0$ we define a notion of connection $\nabla \colon \mathbf{R}\Gamma(X,\mathrm{Ker}…
We study silting objects over derived preprojective algebras of acyclic quivers by giving a direct relationship between silting objects, spherical twist functors and mutations. Especially, for a Dynkin quiver, we establish a bijection…
Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately…
We study representations of Temperley-Lieb algebras associated with the transfer matrix formulation of statistical mechanics on arbitrary lattices. We first discuss a new hyperfinite algebra, the Diagram algebra $D_{\underline{n}}(Q)$,…