Related papers: Koszulity for skew PBW extensions over fields

For a Koszul operad $\mathcal{P}$, there are several existing approaches to the notion of a homotopy between homotopy morphisms of homotopy $\mathcal{P}$-algebras. Some of those approaches are known to give rise to the same notions. We…

The Batalin-Vilkovisky formulation of a general local gauge theory can be encoded in the structure of a so-called presymplectic gauge PDE -- an almost-$Q$ bundle over the spacetime exterior algebra, equipped with a compatible presymplectic…

Let $a$ and $b$ be two integers such that $2\le a<b$. In this article we define the notion of $(a,b)$-Koszul algebra as a generalization of $N$-Koszul algebras. We also exhibit examples and we provide a minimal graded projective resolution…

It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are, in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the classical Koszul and higher…

We construct a Koszul complex in the category of left skew polynomial rings associated to a flat endomorphism that provides a finite free resolution of an ideal generated by a Koszul regular sequence.

We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul which asserts that for a compact…

Using reduction to positive characteristic and the method of Frobenius splitting of diagonals, due to Mehta and Ramanathan, it is shown that homogeneous coordinate rings for either proper and smooth toric varieties or Schubert varieties are…

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…

The $N$-Koszul algebras are $N$-homogeneous algebras which satisfy an homological property. These algebras are characterised by their Koszul complex: an $N$-homogeneous algebra is $N$-Koszul if and only if its Koszul complex is acyclic.…

Given a hypersurface singularity (not necessarily isolated) with a finite abelian group action, we develop a method to define an explicit product structure on the twisted Koszul algebra (whose invariant subalgebra is the orbifold Koszul…

Koszul property was generalized to homogeneous algebras of degree N>2 in [5], and related to N-complexes in [7]. We show that if the N-homogeneous algebra A is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can…

Let $\alpha$ be a quadratic Poisson bivector on a vector space $V$. Then one can also consider $\alpha$ as a quadratic Poisson bivector on the vector space $V^*[1]$. Fixed a universal deformation quantization (prediction some weights to all…

In this note, it is proved that a graphs is $(2K_2,P_4)$-free if and only if its edge ring is universally Koszul. Using properties of this family of graphs, we show that Universally Koszul algebras defined by graphs have linear minimal free…

The aim of this paper is to investigate a general notion of $\sigma$-PBW extensions over Armendariz rings. As an application, the properties of being Baer, quasi-Baer, p.p. and p.q.-Baer are established for these extensions. We generalize…

Let $V$ be a projective hypersurface having only isolated singularities. We show that these singularities are weighted homogeneous if and only if the Koszul syzygies among the partial derivatives of an equation for $V$ are exactly the…

Let S=K[x_1,...,x_n] be a polynomial ring over a field K and I a homogeneous ideal in S generated by a regular sequence f_1,f_2,...,f_k of homogeneous forms of degree d. We study a generalization of a result of Conca, Herzog, Trung, and…

In this paper we define the algebraic sets and the ideal of points for bijective skew PBW extensions with coefficients in left Noetherian domains. Some properties of affine algebraic sets of commutative algebraic geometry will be extended,…

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 a certain splitting condition. In this paper we develop a generalized Koszul theory…

In this paper we discuss for skew $PBW$ extensions the famous Dixmier problem formulated by Jacques Dixmier in 1968. The skew $PBW$ extensions are noncommutative rings of polynomial type and covers several algebras and rings arising in…

We give a complete picture of the interaction between Koszul and Ringel dualities for quasi-hereditary algebras admitting linear tilting (co)resolutions of standard and costandard modules. We show that such algebras are Koszul, that the…