Related papers: Koszul complex over skew polynomial rings

Given an elementary simple-minded collection in the derived category of a non-positive dg algebra with finite-dimensional total cohomology, we construct a silting object via Koszul duality.

We present a procedure that constructs, in a combinatorial manner, a chain complex of free modules over a polynomial ring in finitely many variables, modulo an ideal generated by quadratic monomials. Applying this procedure to two specific…

We study some spectral sequences associated with a locally free $\mathcal O_X$-module $\mathcal A$ which has a Lie algebroid structure. Here $X$ is either a complex manifold or a regular scheme over an algebraically closed field $k$. One…

As the binomial edge ideal of a graph is always generated by homogeneous quadratic polynomials corresponding to the edges of the graph, the question of when a binomial edge ideal defines a Koszul algebra has been studied by many authors…

It has been shown recently, in a joint work with Michel Dubois-Violette and Marc Wambst (see math.QA/0203035), that Koszul property of $N$-homogeneous algebras (as defined in the original paper) becomes natural in a $N$-complex setting. A…

Let $K\to U(V)$ be a unitary representation of the compact Lie group $K$. Then there is a canonical moment mapping $\rho\colon V\to\mathfrak k^*$. We have the Koszul complex ${\mathcal K}(\rho,\mathcal C^\infty(V))$ of the component…

We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain…

We establish formulas for computation of the higher algebraic $K$-groups of the endomorphism rings of objects linked by a morphism in an additive category. Let ${\mathcal C}$ be an additive category, and let $Y\ra X$ be a covariant morphism…

This work concerns commutative algebras of the form $R=Q/I$, where $Q$ is a standard graded polynomial ring and $I$ is a homogenous ideal in $Q$. It has been proposed that when $R$ is Koszul the $i$th Betti number of $R$ over $Q$ is at most…

In this paper we continue the study (initiated in a previous article) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general…

We define and investigate a class of Koszul quasi-hereditary algebras for which there is a natural equivalence between the bounded derived category of graded modules and the bounded derived category of graded modules over (a proper version…

Let $\mathfrak g$ be a complex simple Lie algebra and let $\Psi$ be an extremal set of positive roots. One associates with $\Psi$ an infinite dimensional Koszul algebra $\bold S_\Psi^{\lie g}$ which is a graded subalgebra of the locally…

A presheaf of complexes is constructed on a category of weighted finite subsets of a fixed Euclidean space. To each object, a Koszul complex is assigned which resolves the coordinate ring of least squares solutions on that data set for a…

This works concerns cohomological support varieties of modules over commutative local rings. The main result is that the support of a derived tensor product of a pair of differential graded modules over a Koszul complex is the join of the…

We introduce regular sequences and associated Koszul resolutions for monoids in the category of functors over an essentially small linear symmetric monoidal category. Next we define polynomials over such monoids. We compute the Hochschild…

We construct the so-called polar complex for an arbitrary locally free sheaf on a smooth variety over a field of characteristic zero. This complex is built from logarithmic forms on all irreducible subvarieties with values in a locally free…

Let $k$ be an algebraically closed field of characteristic $0$. Let $X$ be a $2\times e$ matrix of linear forms over a polynomial ring $k[\mathsf{x}_1, \ldots,\mathsf{x}_n]$ (where $e,n\ge 1$). We prove that the determinantal ring $R =…

We establish that the dioperad $Y^{(n)}$, encoding bialgebras with a product of degree zero, a coproduct of degree $(1-n)$ and a rank three cyclic tensor, which satisfy a deformed version of the balanced infinitesimal bialgebra condition,…

We give a new short proof that the wheeled operad of unimodular Lie algebras is Koszul and use this to explicitly construct its minimal resolution. A representation of this resolution in a finite dimensional vector space V we call a…

We introduce a notion of Koszul A-infinity algebra that generalizes Priddy's notion of a Koszul algebra and we use it to construct small A-infinity algebra models for Hochschild cochains. As an application, this yields new techniques for…