Related papers: Extension Groups for DG Modules

Let A be an artin algebra. An A-module M is semi-Gorenstein-projective provided that Ext^i(M,A) = 0 for all i > 0. If M is Gorenstein-projective, then both M and its A-dual M* are semi-Gorenstein projective. As we have shown recently, the…

Let $B = A< X | dX=t >$ be an extended DG algebra by the adjunction of variable of positive even degree $n$, and let $N$ be a semi-free DG $B$-module that is assumed to be bounded below as a graded module. We prove in this paper that $N$ is…

We apply geometric techniques from representation theory to the study of homologically finite differential graded (DG) modules $M$ over a finite dimensional, positively graded, commutative DG algebra $U$. In particular, in this setting we…

We consider the semigroup $Ext(A,B)$ of extensions of a separable C*-algebra $A$ by a stable C*-algebra $B$ modulo unitary equivalence and modulo asymptotically split extensions. This semigroup contains the group $Ext^{-1/2}(A,B)$ of…

To develop a constructive description of $\mathrm{Ext}$ in categories of coherent sheaves over certain schemes, we establish a binatural isomorphism between the $\mathrm{Ext}$-groups in Serre quotient categories $\mathcal{A}/\mathcal{C}$…

Let n be a positive integer, and let A be a strongly commutative differential graded (DG) algebra over a commutative ring R. Assume that (a) B=A[X_1,...,X_n] is a polynomial extension of A, where X_1,...,X_n are variables of positive…

This paper generalises a result for upper triangular matrix rings to the situation of upper triangular matrix DGA's. An upper triangular matrix DGA has the form (R,S,M) where R and S are differential graded algebras and M is a…

We define and characterise completely dg-separable dg-extensions $\varphi:(A,d_A)\rightarrow (B,d_B)$. We completely characterise the case of graded commutative dg-division algebras in characteristic different from $2$. We prove that for a…

Recently, Yekutieli introduced projective dimension and injective dimension of DG-modules by generalizing the characterization of projective dimension and injective dimension of ordinary modules by vanishing of Ext-group. In this paper, we…

Given a complex semisimple Lie algebra ${\mathfrak g}$ and a commutative ${\mathbb C}$-algebra $A$, let ${\mathfrak g}[A] = {\mathfrak g} \otimes A$ be the corresponding generalized current algebra. In this paper we explore questions…

Let $KG$ be a group algebra with $G$ a finite group and $K$ a field and $M$ an indecomposable $KG$-module. We pose the question, whether $Ext_{KG}^1(M,M) \neq 0$ implies that $Ext_{KG}^i(M,M) \neq 0$ for all $i \geq 1$. We give a positive…

The semigroups of unital extensions of separable $C^\ast$-algebras come in two flavours: a strong and a weak version. By the unital $\mathrm{Ext}$-groups, we mean the groups of invertible elements in these semigroups. We use the unital…

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437--445 and J. Algebra Appl., 8 (2009), 219--227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective…

In this article we are examining extensions and some basic diagrammatic properties of modules, in both cases from a new, "virtual" point of view. As natural background for investigating the kind of problems we are dealing with, the virtual…

We exhibit an isomorphism of associative algebras between the $\operatorname{Ext}$-algebra $\operatorname{Ext}_\Lambda^\ast(\Delta,\Delta)$ of standard modules over the dual extension algebra $\Lambda$ of two directed algebras $B$ and $A$…

Let $\A$ be a unital separable nuclear $C^*$--algebra which belongs to the bootstrap category $\N$ and $\B$ be a separable stable $C^*$--algebra. In this paper, we consider the group $\Ext_u(\A,\B)$ consisting of the unitary equivalence…

In this paper, we study the Ext-algebras of graded skew extensions. For a connected graded algebra $A$ and a graded automorphism $\sigma$, we analyze the Yoneda product of the Ext-algebra of graded skew extension $A[z;\sigma]$, and prove…

Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…

The notion of naive liftability of DG modules is introduced in [9] and [10]. In this paper, we study the obstruction to naive liftability along extensions $A\to B$ of DG algebras, where $B$ is projective as an underlying graded $A$-module.…

There are well known identities that involve the Ext bifunctor, coproducts, and products in Ab4 and Ab4* abelian categories with enough projectives and enough injectives. Namely, for every such category $\mathcal{A}$, the isomorphisms…