Related papers: Extensions realizing affine datum : central extens…
We describe the split extension classifiers in the semi-abelian category of cocommutative Hopf algebras over an algebraically closed field of characteristic zero. The categorical notions of centralizer and of center in the category of…
We study noncommutative principal bundles (Hopf-Galois extensions) in the context of coquasitriangular Hopf algebras and their monoidal category of comodule algebras. When the total space is quasi-commutative, and thus the base space…
We introduce the notion of compatible actions in the context of split extensions of finite dimensional Lie algebras over a field. Using compatible actions, we construct a new resolution to compute the cohomology of semi-direct products of…
We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…
We introduce the Hochschild extensions of dg algebras, which are $A_\infty$-algebras. We show that all exact Hochschild extensions are symmetric Hochschild extensions, more precisely, every exact Hochschild extension of a finite dimensional…
An algebra extension $A \| B$ is right depth two in this paper if its tensor-square is $A$-$B$-isomorphic to a direct summand of any (not necessarily finite) direct sum of $A$ with itself. For example, normal subgroups of infinite groups,…
Let $X$ be a cohomologically $(n-1)$-complete complex manifold of dimension $n\geq 2$. We prove a vanishing result for the Bott-Chern cohomology group of type $(1, 1)$ with compact support in $X$, which combined with the well-known…
The variety of skew braces contains several interesting subcategories as subvarieties, as for instance the varieties of radical rings, of groups and of abelian groups. In this article the methods of non-abelian homological algebra are…
We explore the notion of representation of an affine extension of an abelian variety -- such an extension is a faithfully flat affine morphism of $\Bbbk$-group schemes $q:G\to A$, where $A$ is an abelian variety. We characterize the…
We give a necessary and sufficient condition for two Hopf algebras presented as central extensions to be isomorphic, in a suitable setting. We then study the question of isomorphism between the Hopf algebras constructed in 0707.0070v1 as…
Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic…
Let A be a Banach algebra and let X be a Banach A -bimodule. In studying the bounded Hochschild cohomology groups H^1(A,X) it is often useful to extend a given derivation D: A-> X to a Banach algebra B containing A as an ideal, thereby…
The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $\mathfrak g\otimes \mathbb C[t,t^{-1},u|u^2=(t^2-b^2)(t^2-c^2)]$, appearing…
We prove several basic extension theorems for reductive group schemes. We also prove that each Lie algebra with a perfect Killing form over a commutative $\dbZ$-algebra, is the Lie algebra of an adjoint group scheme.
The notions of Hom-coring, Hom-entwining structure and associated entwined Hom-module are introduced. A theorem regarding base ring extension of a Hom-coring is proven and then is used to acquire the Hom-version of Sweedler coring.…
We study the homological algebra in the category $\mathcal{P}_p$ of strict polynomial functors of degree $p$ over a field of positive characteristic $p$. We determine the decomposition matrix of our category and we calculate the Ext-groups…
In this paper we discuss metric theory associated with the affine (inhomogeneous) linear forms in the so called doubly metric settings within the classical and the mixed setups. We consider the system of affine forms given by $\qq\mapsto…
We introduce the notion of affinizations and R-matrices for arbitrary quiver Hekcke algebras. We show that they enjoy similar properties to those for symmetric quiver Hecke algebras. We next define the notion of a duality datum and…
As a generalisation of Graham and Lehrer's cellular algebras, affine cellular algebras have been introduced in [12] in order to treat affine versions of diagram algebras like affine Hecke algebras of type A and affine Temperley-Lieb…
The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type structure and fits perfectly with simultaneous…