Related papers: Derived intersections and free dg-Lie algebroids
We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended…
In this paper, we first recall the construction of a twisted pre-Lie algebra structure on the species of finite connected topological spaces. Then we construct the corresponding nonassociative permutative coproduct, and we prove that the…
We introduce dg Lie algebras controlling the deformations of vertex algebras and vertex Poisson algebras, utilizing the notion of operadic dg Lie algebra and the theory of chiral algebra. In terms of those dg Lie algebras, we formulate the…
Let $V$ be a vertex algebra and $g$ an automorphism of $V$ of order $T$. We construct a sequence of associative algebras $\tilde{A}_{g,n}(V )$ for any $n\in(1/T)\mathbb{N}$, which are not depend on the conformal structure of $V$. We show…
Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that…
This paper contains an elementary proof of the existence of the classical model structure on the category of unbounded DG-Lie algebras over a field of characteristic zero, with an emphasis on the properties of free and semifree extensions,…
In the present paper, we propose the concepts of weighted differential ($q$-tri)dendriform algebras and give some basic properties of them. The corresponding free objects are constructed, in both the commutative and noncommutative contexts.
The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with universal central extensions. Then, using a…
We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely…
We present a general construction of the derived category of an algebra over an operad and establish its invariance properties. A central role is played by the enveloping operad of an algebra over an operad.
The purpose of this paper is to develop a suitable notion of continuous L_infinity morphism between DG Lie algebras, and to study twists of such morphisms.
We introduce the notion of a non--linear Lie conformal superalgebra and prove a PBW theorem for its universal enveloping vertex algebra. We also show that conversely any graded freely generated vertex algebra is the universal enveloping…
Divisible design digraphs are constructed from skew balanced generalized weighing matrices and generalized Hadamard matrices. Commutative and non-commutative association schemes are shown to be attached to the constructed divisible design…
Free differential algebras (FDA's) provide an algebraic setting for field theories with antisymmetric tensors. The "presentation" of FDA's generalizes the Cartan-Maurer equations of ordinary Lie algebras, by incorporating p-form potentials.…
In this article we develop an approach to deformations of the Witt and Virasoro algebras based on $\sigma$-derivations. We show that $\sigma$-twisted Jacobi type identity holds for generators of such deformations. For the $\sigma$-twisted…
Algebraic scheme for constructing deformations of structure constants for associative algebras generated by a deformation driving algebras (DDAs) is discussed. An ideal of left divisors of zero plays a central role in this construction.…
Deformed $\W$--algebra $\W_{q,t}(\g)$ associated to an arbitrary simple Lie algebra $\g$ is defined together with its free field realizations and the screening operators. Explicit formulas are given for generators of $\W_{q,t}(\g)$ when…
We apply the effective integration theory of Lie-graph algebras, developed recently by the authors, to the deformation and homotopy theories of types of bialgebras, that is structures controlled by a properad, like associative bialgebras,…
We establish the Gr\"obner-Shirshov bases theory for differential Lie $\Omega$-algebras. As an application, we give a linear basis of a free differential Lie Rota-Baxter algebra on a set.
In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of Poisson Hopf algebras in the differential graded setting. The structures on the universal…