Related papers: A generalized Koszul property for skew PBW extensi…
In this paper we compute the center of many noncommutative algebras that can be interpreted as skew $PBW$ extensions. We show that, under some natural assumptions on the parameters that define the extension, either the center is trivial,…
In this short paper we study for the skew PBW (Poincar\'e-Birkhoff-Witt) extensions some homological properties arising in non-commutative algebraic geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and strongly…
In this paper we discuss some open problems of non-commutative algebra and non-commutative algebraic geometry from the approach of skew $PBW$ extensions and semi-graded rings. More exactly, we will analyze the isomorphism arising in the…
We present an easily applicable sufficient condition for standard Koszul algebras to be Koszul with respect to $\Delta$. If a quasi-hereditary algebra $\L$ is Koszul with respect to $\Delta$, then $\L$ and the Yoneda extension algebra of…
The Koszul homology algebra of a commutative local (or graded) ring $R$ tends to reflect important information about the ring $R$ and its properties. In fact, certain classes of rings are characterized by the algebra structure on their…
In this article we give a description for the centralizer of the coefficient ring $R$ in the skew PBW extension $\sigma(R)<x_1,x_2,\cdots,x_n>.$ We give an explicit description in the quasi-commutative case and state a necessary condition…
In this paper we extend some results obtained by Artamonov and Sabitov for quantum polynomials to skew quantum polynomials and quasi-commutative bijective skew PBW extensions. Moreover, we find a counterexample to the conjecture proposed in…
We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis…
The aim of this paper is to develop the theory of skew Armendariz and quasi-Armendariz modules over skew PBW extensions. We generalize the results of several works in the literature concerning Ore extensions to another non-commutative rings…
There are many structures (algebras, categories, etc) with natural gradings such that the degree 0 components are not semisimple. Particular examples include tensor algebras with non-semisimple degree 0 parts, extension algebras of standard…
Graded quasi-commutative skew PBW extensions are isomorphic to graded iterated Ore extensions of endomorphism type, whence graded quasi-commutative skew PBW extensions with coefficients in AS-regular algebras are skew Calabi-Yau and the…
This article is concerned with graded modules M with linear resolutions over a standard graded algebra R. It is proved that if such an M has Hilbert series $H_M(s)$ of the form $ps^d+qs^{d+1}$, then the algebra R is Koszul; if, in addition,…
From symplectic reflection algebras, some algebras are naturally introduced. We show that these algebras are non-homogeneous N-Koszul algebras, through a PBW theorem.
We generalize the theory of Koszul complexes and Koszul algebras (in particular, Koszul duality between symmetric and exterior algebras) to symmetric tensor categories. In characteristic $p\ge 5$, this theory exhibits peculiar effects, not…
Under certain conditions, a filtration on an augmented algebra A admits a related filtration on the Yoneda algebra E(A) := Ext_A(K, K). We show that there exists a bigraded algebra monomorphism from gr E(A) to E_Gr(gr A), where E_Gr(gr A)…
In this paper we introduce the semi-graded rings, which extend graded rings and skew PBW extensions. For this new type of non-commutative rings we will discuss some basic problems of non-commutative algebraic geometry. In particular, we…
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…
We give Braverman-Gaitsgory style conditions for general PBW deformations of skew group algebras formed from finite groups acting on Koszul algebras. When the characteristic divides the order of the group, this includes deformations of the…
We extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the…
In this paper, we study the Koszul property of the homogeneous coordinate ring of a generic collection of lines in $\mathbb{P}^n$ and the homogeneous coordinate ring of a collection of lines in general linear position in $\mathbb{P}^n.$ We…