Related papers: Generalized Koszul properties for augmented algebr…

Let $R=\oplus_{\Gamma\in\Gamma}R_{\gamma}$ be a $\Gamma$-graded $K$-algebra over a field $K$, where $\Gamma$ is a totally ordered semigroup, and let $I$ be an ideal of $R$. Considering the $\Gamma$-grading filtration $FR$ of $R$ and the…

Let $A$ be a finite dimensional $k$-algebra standardly stratified for a partial order $\leqslant$ and $\Delta$ be the direct sum of all standard modules. In this paper we study the extension algebra $E= \text{Ext}_A^{\ast} (\Delta, \Delta)$…

Let A be a connected graded noncommutative monomial algebra. We associate to A a finite graph \Gamma(A) called the CPS graph of A. Finiteness properties of the Yoneda algebra Ext_A(k,k) including Noetherianity, finite GK dimension, and…

We define a notion of Koszul dual of a monoid object in a monoidal biclosed model category. Our construction generalizes the classic Yoneda algebra $Ext_A(k,k)$. We apply this general construction to define the Koszul dual of a category…

Let A and A! be dual Koszul algebras. By Positselski a filtered algebra U with gr U = A is Koszul dual to differential graded algebra (A!,d). We relate the module categories of this dual pair by a tensor-Hom adjunction. This descends to…

Given a quasi-hereditary algebra $B$, we present conditions which guarantee that the algebra $\gr B$ obtained by grading $B$ by its radical filtration is Koszul and at the same time inherits the quasi-hereditary property and other good…

We give a description of the connected graded algebras which are finitely generated and presented of global dimension 2 or 3 and which are Gorenstein. These algebras are constructed from multilinear forms. We generalize the construction by…

In this paper, we introduce the class of finitely semi-graded algebras which extends the connected graded algebras finitely generated in degree one. The Koszul behavior of finitely semi-graded algebras is investigated by the distributivity…

Generalized \dK modules are introduced to solve an open problem: the odd Ext-module $\Eod(M)$ of a \dK module $M$ over a $d$-Koszul algebra $\m$ is a \K module over the even Yoneda algebra $\Eev(\m)$.

We define generalized Koszul modules and rings and develop a generalized Koszul theory for $\mathbb{N}$-graded rings with the degree zero part noetherian semiperfect. This theory specializes to the classical Koszul theory for graded rings…

Let $A$ be a graded algebra. In this paper we develop a generalized Koszul theory by assuming that $A_0$ is self-injective instead of semisimple and generalize many classical results. The application of this generalized theory to directed…

We construct a generalization of Koszul duality in the sense of Keller--Lef\`evre for not necessarily augmented algebras. This duality is closely related to classical Morita duality and specializes to it in certain cases.

We generalise Koszul and D-Koszul algebras by introducing a class of graded algebras called (D,A)-stacked algebras. We give a characterisation of (D,A)-stacked algebras and show that their Ext algebra is finitely generated as an algebra in…

The algebra of basic covers of a graph G, denoted by \A(G), was introduced by Juergen Herzog as a suitable quotient of the vertex cover algebra. In this paper we show that if the graph is bipartite then \A(G) is a homogeneous algebra with…

Various concepts associated with quadratic algebras admit natural generalizations when the quadratic algebras are replaced by graded algebras which are finitely generated in degree 1 with homogeneous relations of degree N. Such algebras are…

We show that the graded maximal ideal of a graded $K$-algebra $R$ has linear quotients for a suitable choice and order of its generators if the defining ideal of $R$ has a quadratic Gr\"obner basis with respect to the reverse lexicographic…

This paper investigates if a differential graded algebra can have more than one $A_\infty$-structure extending the given differential graded algebra structure. We give a sufficient condition for uniqueness of such an $A_\infty$-structure up…

Let $A = \bigoplus_{i \geqslant 0} A_i$ be a graded locally finite $k$-algebra such that $A_0$ is an arbitrary finite-dimensional algebra satisfying some splitting condition. In this paper we develop a generalized Koszul theory generalizing…

We study some formality criteria for differential graded algebras over differential graded operads. This unifies and generalizes other known approaches like the ones by Manetti and Kaledin. In particular, we construct general operadic…

This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic…