Related papers: Dg-separable dg-extensions

We prove that the derived category of a Grothendieck abelian category has a unique dg enhancement. Under some additional assumptions, we show that the same result holds true for its subcategory of compact objects. As a consequence, we…

Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms of central simple graded-division…

Inspired by the intrinsic formality of graded algebras, we prove a necessary and sufficient condition for strongly uniqueness of DG-enhancements. This approach offers a generalization to linearity over any commutative ring. In particular,…

We define a $p$-DG structure on a deformation of Webster algebra of type $A_1$ and its splitter bimodules.

Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…

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…

Let A be a finite-dimensional, self-injective algebra, graded in non-positive degree. We define A-dgstab, the differential graded stable category of A, to be the quotient of the bounded derived category of dg-modules by the thick…

Given a commutative algebra $A$ and a quotient $A$-algebra $A/I$, we construct a resolution of $A/I$ as an $A$-module such that it is also a differential graded (dg) algebra with divided powers (PD). This construction makes use of symmetric…

We study Ore localisation of differential graded algebras. Further we define dg-prime rings, dg-semiprime rings, and study the dg-nil radical of dg-rings. Then, we define dg-essential submodules, dg-uniform dimension, and apply all this to…

A graph $G$ is said to be $k$-extendable if every matching of size $k$ in $G$ can be extended to a perfect matching of $G$, where $k$ is a positive integer. We say $G$ is $1$-excludable if for every edge $e$ of $G$, there exists a perfect…

Let G be the group of L-rational points of a connected split reductive group over a finite extension L of Q_p. We show that formal models of the algebraic flag variety X of G are D-affine for certain sheaves of arithmetic differential…

We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to…

We classify group gradings on the simple Lie algebra $L$ of type $D_4$ over an algebraically closed field of characteristic different from 2: fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism. For…

Let $(\mathfrak{g},[p])$ be a finite dimensional restricted Lie algebra over a perfect field $\mathbbm{k}$ of characteristic $p\!\ge \!3$. By combining methods from recent work of Benson-Carlson \cite{BC20} with those of \cite{CF21,Fa17} we…

We compute the {\Omega}^1(G) invariant when 1 {\to} H {\to} G {\to} K {\to} 1 is a split short exact sequence. We use this result to compute the invariant for pure and full braid groups on compact surfaces. Applications to twisted conjugacy…

We give a complete classification of reductive symmetric pairs (g, h) with the following property: there exists at least one infinite-dimensional irreducible (g,K)-module X that is discretely decomposable as an (h,H \cap K)-module. We…

Let $Q$ be a local ring with maximal ideal $\mathfrak{n}$ and let $f,g\in \mathfrak{n}\smallsetminus\mathfrak{n}^2$ with $fg=0$. When $M$ is a finite $Q$-module with $fM=0$, we show that a minimal free resolution of $M$ over $Q$ has a…

Let $k$ be an algebraically closed field of characteristic $p>0$, let G=GL_n be the general linear group over $k$, let g=gl_n be its Lie algebra and let $D_s$ be subalgebra of the divided power algebra of g^* spanned by the divided power…

We describe cohomological conditions that are necessary and sufficient for the existence of balanced dualizing dg-modules, generalizing a theorem of Van den Bergh for balanced dualizing complexes over graded algebras. As a consequence, we…

A DG algebras $A$ over a field $k$ with $H(A)$ connected and $H_{<0}(A)=0$ has a unique up to isomorphism DG module $K$ with $H(K)\cong k$. It is proved that if $H(A)$ is degreewise finite, then $RHom_A(?,K): D^{df}_{+}(A)^{op} \equiv…