Related papers: Quadratic algebras with Ext algebras generated in …

Let G be a topological group such that its homology H(G) with coefficients in a principal ideal domain R is an exterior algebra, generated in odd degrees. We show that the singular cochain functor carries the duality between G-spaces and…

We investigate compatibility of gradings for an almost Koszul or Koszul algebra $R$ that is also the higher preprojective algebra $\Pi_{n+1}(A)$ of an $n$-hereditary algebra $A$. For an $n$-representation finite algebra $A$, we show that…

We associate to a sufficiently generic oriented matroid program and choice of linear system of parameters a finite dimensional algebra, whose representation theory is analogous to blocks of Bernstein--Gelfand--Gelfand category $\mathcal O$.…

We introduce Koszul modules associated with (graded) Kac-Moody Lie algebras. We provide a precise criterion for when these modules are of finite length. As an exemplary application we deduce a bound on the dimension of the second graded…

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…

Let $k$ be a field of characteristic $0$. Using the method of idealization, we show that there is a non-Koszul, quadratic, Artinian, Gorenstein, standard graded $k$-algebra of regularity $3$ and codimension $8$, answering a question of…

We prove that the Milnor ring of any (one-dimensional) local or global field K modulo a prime number l is a Koszul algebra over Z/l. Under mild assumptions that are only needed in the case l=2, we also prove various module Koszulity…

In previous work, the authors introduced the notion of Q-Koszul algebras, as a tool to "model" module categories for semisimple algebraic groups over fields of large characteristics. Here we suggest the model extends to small…

We define the $m$th Veronese power of a weight graded operad $\mathcal{P}$ to be its suboperad $\mathcal{P}^{[m]}$ generated by operations of weight $m$. It turns out that, unlike Veronese powers of associative algebras, homological…

In this paper, we show that for a Koszul $n$-homogeneous algebra $\Lambda$, the quadratic dual of certain twisted trivial extension is the $(n+1)$-preprojective algebra of its quadratic dual, that is, $ (\Delta_{\nu}\Lambda)^{!,op}…

We study a class of noncommutative surfaces and their higher dimensional analogues which provide answers to several open questions in noncommutative projective geometry. Specifically, we give the first known graded algebras which are…

We consider nonsymmetric operads with two binary operations satisfying relations in arity 3; hence these operads are quadratic, and so we can investigate Koszul duality. We first consider operations which are nonassociative (not necessarily…

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prove a theorem that affords a presentation by generators and…

Generalized \dK modules are introduced to solve an open problem: the odd Ext-module $\Eod(M)$ of a \dK module $M$ over a $d$-Koszul algebra $\m$ is a \K module over the even Yoneda algebra $\Eev(\m)$.

We show that there exists a natural non-degenerate pairing of the homomorphism space between two neighbor standard modules over a quasi-hereditary algebra with the first extension space between the corresponding costandard modules and vise…

We study weakly symmetric special biserial algebras of infinite representation type. We show that usually some socle deformation of such an algebra has non-periodic bounded modules. The exceptions are precisely the algebras whose Brauer…

Extended Khovanov arc algebras $\mathrm{K}_m^n$ are graded associative algebras which naturally appear in a variety of contexts, from knot and link homology, low-dimensional topology and topological quantum field theory to representation…

Given any Koszul algebra of finite global dimension one can define a new algebra, which we call a higher zigzag algebra, as a twisted trivial extension of the Koszul dual of our original algebra. If our original algebra is the path algebra…

In this paper we study symmetric Leibniz and related algebras, namely symmetric dialgebras and symmetric Perm-algebras. We also calculate their Koszul duals, if not known. This will give us Lie-admissible algebras and new types of algebras,…

Let $A$ be an associative algebra graded by a finite group $G$ over a field ${F}$ of characteristic zero. One associates to $A$ the sequence of $G$-graded codimensions $c_n^G(A)$, $n=1,2,\ldots$, which measures the growth of the polynomial…