Related papers: Koszulness, Krull Dimension and Other Properties o…

We define a basic class of algebras which we call homotopy path algebras. We find that such algebras always admit a cellular resolution and detail the intimate relationship between these algebras, stratifications of topological spaces, and…

We define a local homomorphism $(Q,k)\to (R,\ell)$ to be Koszul if its derived fiber $R \otimes^{\mathsf{L}}_Q k$ is formal, and if $\operatorname{Tor}^Q(R,k)$ is Koszul in the classical sense. This recovers the classical definition when…

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…

Given an ample, Hausdorff groupoid $\mathcal{G}$, and a unital commutative ring $R$, we consider the Steinberg algebra $A_R(\mathcal {G})$. First we prove a uniqueness theorem for this algebra and then, when $\mathcal{G}$ is graded by a…

In this paper, we introduce a new notion of algebra over a linear $\infty$-operad and a corresponding notion of coalgebra over an $\infty$-cooperad. We next extend the Koszul duality between linear $\infty$-operads and linear…

A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem (MAX H-COL) are edge-weighted graphs G and the objective is to find…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional algebra A and AG is the associated skew group algebra. The author with S. Trepode and A. G. Chaio introduced the notion…

For a finite dimensional monomial algebra $\Lambda$ over a field $K$ we show that the Hochschild cohomology ring of $\Lambda$ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated $K$-algebra of…

We extend to one dimensional quotients the result of A. Conca and S. Murai on the convexity of the regularity of Koszul cycles. By providing a relation between the regularity of Koszul cycles and Koszul homologies we prove a sharp…

Let $G$ be an unmixed bipartite graph of dimension $d-1$. Assume that $K_{n,n}$, with $n\ge 2$, is a maximal complete bipartite subgraph of $G$ of minimum dimension. Then $G$ is Cohen-Macaulay in codimension $d-n+1$. This generalizes a…

We present the Gerstenhaber algebra structure on the Hochschild cohomology of Koszul algebras defined by quivers and relations using the idea of homotopy liftings. E.L. Green, G. Hartman, E.N. Marcos and O. Solberg provided a canonical way…

Koszul algebras with quadratic Groebner bases, called strong Koszul algebras, are studied. We introduce affine algebraic varieties whose points are in one-to-one correspondence with certain strong Koszul algebras and we investigate the…

In this paper we investigate the Rees algebras of squarefree monomial ideals $I \subset S=K[x_1,\dots,x_n]$ generated in degree $n-2$, where $K$ is a field. Every such ideal arises as the complementary edge ideal $I_c(G)$ of a finite simple…

A differential graded (DG for short) free algebra $\mathcal{A}$ is a connected cochain DG algebra such that its underlying graded algebra is $$\mathcal{A}^{\#}=\k\langle x_1,x_2,\cdots, x_n\rangle,\,\, \text{with}\,\, |x_i|=1,\,\, \forall…

We give examples of Koszul rings that arise naturally in algebraic geometry. In the first part, we prove a general result on Koszul property associated to an ample line bundle on a projective variety. Specifically, we show how Koszul…

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,…

For a system of non-homogeneous polynomials it was constructed explicit complex morphism of a dual complex to the Koszul complex into the Koszul complex. If the ideal of these polynomials is 0-dimensional, then this mapping is a homotopic…

Motivated by the representation theory of symplectic reflection algebras, deformed preprojective algebras, and graded Hecke algebras, we consider filtered algebras $U$ whose associated graded is Koszul. The Koszul dual of $U$, as defined by…

Let Q be a regular local ring of dimension 3. We show how to trim a Gorenstein ideal in Q to obtain an ideal that defines a quotient ring that is close to Gorenstein in the sense that its Koszul homology algebra is a Poincare duality…

The Koszul homology of modules of the polynomial ring $R$ is a central object in commutative algebra.It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we…