Related papers: Derived Equivalences of Upper Triangular Different…
A triangular matrix ring A is defined by a triplet (R,S,M) where R and S are rings and M is an S-R-bimodule. In the main theorem of this paper we show that if T is a tilting S-module, then under certain homological conditions on M as an…
This paper focuses on defining an analog of differential-graded triangular matrix algebra in the context of differential-graded categories. Given two dg-categories $\mathcal{U}$ and $\mathcal{T}$ and $M \in \text{DgMod}(\mathcal{U} \otimes…
In this paper, we will consider derived equivalences for differential graded endomorphism algebras by Keller's approaches. First we construct derived equivalences of differential graded algebras which are endomorphism algebras of the…
Based on work presented in [4], we define $S^2$-Upper Triangular Matrices and $S^2$-Lower Triangular Matrices, two special types of $d\times d(2d-1)$ matrices generalizing Upper and Lower Triangular Matrices, respectively. Then, we show…
Let $\mathcal A$ and $\mathcal B$ be unital rings and $\mathcal M$ be a $(\mathcal A, \mathcal B)$-bimodule, which is faithful as a left $\mathcal A$-module and also as a right $\mathcal B$-module. Let ${\mathcal U}={\rm Tri}(\mathcal A,…
Let R and S be differential graded algebras. In this paper we give a characterisation of when a differential graded R-S-bimodule M induces a full embedding of derived categories M\otimes - :D(S)--> D(R). In particular, this characterisation…
The main result of this paper is that there is sometimes a triangulated equivalence between $D_Q( A )$, the $Q$-shaped derived category of an algebra $A$, and $D( B )$, the classic derived category of a different algebra $B$. By…
We describe the graded isomorphisms of rings of endomorphisms of graded flags over graded division algebras. As a consequence describe the isomorphism classes of upper block triangular matrix algebras (over an algebraically closed field of…
In this paper we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras, and describe…
Recently, Hu and Xi have exhibited derived equivalent endomorphism rings arising from (relative) almost split sequences as well as AR-triangles in triangulated categories. We present a broader class of triangles (in algebraic triangulated…
In this paper, we give a concrete description of the higher homotopy groups (n>0) of the mapping space Map_{Alg}(R,S) for R and S unbounded differential graded algebras (DGA) over a commutative ring k. In the connective case, we describe…
In this paper, we construct derived equivalences between matrix subrings. As applications, we calculate the global dimensions and the finitistic dimensions of some matrix subrings. And we show that the finitistic dimension conjecture holds…
In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra $A$ such that $A_0$ has finite global…
In this paper, we prove the dg affinity of formal deformation algebroid stacks over complex smooth algebraic varieties. For that purpose, we introduce the triangulated category of formal deformation modules which are cohomologically…
Let $A$ be a graded algebra. It is shown that the derived category of dg modules over $A$ (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded $A$-modules.…
We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is…
We extend a theorem of Ladkani concerning derived equivalences between upper-triangular matrix rings from ordinary rings to ring spectra. Our result also extends an analogous theorem of Maycock for differential graded algebras.
Let $M$ and $N$ be differential graded (DG) modules over a positively graded commutative DG algebra $A$. We show that the Ext-groups $\operatorname{Ext}^i_A(M,N)$ defined in terms of semi-projective resolutions are not in general isomorphic…
We prove that, under mild assumptions, the $Q$-shaped derived categories introduced by Holm and J{\o}rgensen are equivalent to derived categories of differential graded bimodules over differential graded categories. This yields new derived…
This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra…