Related papers: Graded algebras and multilinear forms

We give new properties of algebras with finite Gorenstein dimension coinciding with the dominant dimension $\geq 2$, which are called Auslander-Gorenstein algebras in the recent work of Iyama and Solberg, see \cite{IyaSol}. In particular,…

Vatne and Green & Marcos have independently studied the Koszul-like homological properties of graded algebras that have defining relations in degree 2 and exactly one other degree. We contrast these two approaches, answer two questions…

We show that there exist non-Koszul graded algebras that appear to be Koszul up to any given cohomological degree. For any integer m>2 we exhibit a non-commutative quadratic algebra for which the corresponding bigraded Yoneda algebra is…

We study Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. We introduce rank matrices of linear forms for such algebras that represent the ranks of multiplication maps in various degrees. We…

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 math.QA/0506507 I. Gelfand and the authors introduced and studied a new class of algebras associated to directed graphs. In this paper we show that these algebras are Koszul for a large class of layered (i.e. ranked) graphs.

Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…

The rate of a standard graded $K$-algebra $A$ is a measure of the growth of the shifts in a minimal free resolution of $K$ as an $A$-module. In particular $A$ has rate one if and only if it is Koszul. It is known that a generic Artinian…

The so called generalized down-up algebras are revisited from a viewpoint of Gr\"obner basis theory. Particularly it is shown explicitly that generalized down-up algebras are solvable polynomial algebras (provided $\lambda\omega\ne 0$), and…

We consider varieties generated by finite closure algebras whose canonical relations have two levels, and whose restriction to a level is an "extremal" relation, i.e. the identity or the universal relation. The corresponding logics have…

In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra $A$ such that $A_0$ has finite global…

Given an affine hyperplane arrangement with some additional structure, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul…

For any $n$-ary associative algebra we construct a $\Z_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.

Let $H$ be a finite-dimensional connected Hopf algebra over an algebraically closed field $\field$ of characteristic $p>0$. We provide the algebra structure of the associated graded Hopf algebra $\gr H$. Then, we study the case when $H$ is…

We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…

We prove that the algebra of closed differential forms in an (algebraic, formal, or analytic) disk with logarithmic singularities along several coordinate hyperplanes is (both nontopologically and topologically) Koszul. The connection with…

(Partial) Gorenstein silting modules are introduced and investigated. It is shown that for finite dimensional algebras of finite CM-type, partial Gorenstein silting modules are in bijection with {\tau}_G-rigid modules; Gorenstein silting…

Galilean conformal algebras can be constructed by contracting a finite number of conformal algebras, and enjoy truncated $\mathbb{Z}$-graded structures. Here, we present a generalisation of the Galilean contraction procedure, giving rise to…

By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra…

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…