Related papers: Graded and Koszul categories
In this article we classify indecomposable objects of the derived categories of finitely-generated modules over certain infinite-dimensional algebras. The considered class of algebras (which we call nodal algebras) contains such well-known…
A relationship between curved differential algebras and corings is established and explored. In particular it is shown that the category of semi-free curved differential graded algebras is equivalent to the category of corings with…
We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld in \cite{bd}, to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and…
We define a class of quadratic differential algebras which are generated as differential graded algebras by the elements of an Euclidean space. Such a differential algebra is a differential calculus over the quadratic algebra of its…
We show that any upper finite or essentially finite highest weight category where the standard objects have linear projective resolutions and the costandard objects have linear injective resolutions is Koszul. This extends the result of…
We survey the topology which led to the original bar and cobar constructions, for both associative algebras and coalgebras and for Lie algebras and commutative coalgebras. These constructions are often viewed as part of the larger theory of…
The paper deals with the classification of a subclass of finite-dimensional Zinbiel algebras: the naturally graded p-filiform Zinbiel algebras. A Zinbiel algebra is the dual to Leibniz algebra in Koszul sense. We prove that there exists, up…
The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K_2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K_2 algebra would be another K_2 algebra. We show that…
This paper has two parts. The main goal, carried out in Part I, is to survey some recent work by the authors in which "forced" grading constructions have played a significant role in the representation theory of semisimple algebraic groups…
Let $R$ be a Koszul algebra over a field $k$ and $M$ be a linear $R$-module. We study a graded subalgebra $\Delta_M$ of the Ext-algebra $\operatorname{Ext}_R^*(M,M)$ called the diagonal subalgebra and its properties. Applications to the…
Over-extended Kac-Moody algebras contain so-called gradient structures - a gl(d)-covariant level decomposition of the algebra contains strings of modules at different levels that can be interpreted as spatial gradients. We present an…
Suppose that we have a bicomplete closed symmetric monoidal quasi-abelian category $\mathcal{E}$ with enough flat projectives, such as the category of complete bornological spaces $\textbf{CBorn}_k$ or the category of inductive limits of…
We investigate blocks of the Category $\mathcal O$ for the Virasoro algebra over the complex numbers. We demonstrate that the blocks have Kazhdan-Lusztig theories, and that the truncated blocks give rise to interesting Koszul algebras. The…
The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of…
We develop a Koszul-theoretic framework for comparing classical Alexander-type invariants with infinitesimal invariants arising from finite-type commutative differential graded algebra models. The central mechanism is Koszul linearization,…
We discuss recent progress on syzygies of curves, including proofs of Green's and Gonality Conjectures as well as applications of Koszul cycles to the study of the birational geometry of various moduli spaces of curves. We prove a number of…
The aim of this article is to provide a complementary understanding to some results of the second author using the machinery of Koszul complexes, and to explain how this approach can provide a new description of projective derived…
This paper studies the role of dg-Lie algebroids in derived deformation theory. More precisely, we provide an equivalence between the homotopy theories of formal moduli problems and dg-Lie algebroids over a commutative dg-algebra of…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
Classifying isomorphism classes of group gradings on algebras presents a compelling challenge, particularly within the realms of non-simple and infinite-dimensional algebras, which have been relatively unexplored. This study focuses on a…