Related papers: The alternative operad is not Koszul

We introduce the alternating Schur algebra $AS_F(n,d)$ as the commutant of the action of the alternating group $A_d$ on the $d$-fold tensor power of an $n$-dimensional $F$-vector space. When $F$ has characteristic different from $2$, we…

We establish an explicit isomorphism between the associated graded of the filtered chiral operad and the classical operad, which is useful for computing the cohomology of vertex algebras.

We show that modular operads are equivalent to modules over a certain simple properad which we call the Brauer properad. Furthermore, we show that, in this setting, the Feynman transform corresponds to the cobar construction for modules of…

The purpose of this paper is to show how Positselski's relative nonhomogeneous Koszul duality theory applies when studying the linear category underlying the PROP associated to a (non-augmented) operad of a certain form, in particular…

For R=Q/J with Q a commutative graded algebra over a field and J non-zero, we relate the slopes of the minimal resolutions of R over Q and of k=R/R_{+} over R. When Q and R are Koszul and J_1=0 we prove Tor^Q_i(R,k)_j=0 for j>2i, for each…

We provide an algorithmic method for constructing projective resolutions of modules over quotients of path algebras. This algorithm is modified to construct minimal projective resolutions of linear modules over Koszul algebras.

This work concerns the moment map $\mu$ associated with the standard representation of a classical Lie algebra. For applications to deformation quantization it is desirable that $S/(\mu)$, the coordinate algebra of the zero fibre of $\mu$,…

We give an example to show that the main result of [1] is incorrect.

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we…

We establish a twisted version of Skoda's estimate for the Koszul complex from which we get division theorems for the Koszul complex. This generalizes Skoda's division theorem. We also show how to use Skoda triples to produce division…

In previous works, the author described an associative algebra whose $A_\infty$-module categories encode the Heegaard Floer Dehn surgery formulas. In this article, we describe the Koszul dual of this algebra. We construct dualizing…

We investigate operads for various n-ary algebras. As a useful tool we introduce galgalim - analogs of the Lie-hedra for n-ary algebras. We then focus to algebras with one anti-associative operation. We describe the relevant part of the…

In this article we establish a version of Koszul duality for filtered rings arising from $p$-adic Lie groups. Our precise setup is the following. We let $G$ be a uniform pro-$p$ group and consider its completed group algebra…

We define, for a somewhat standard forgetful functor from nonsymmetric operads to weight graded associative algebras, two functorial "enveloping operad" functors, the right inverse and the left adjoint of the forgetful functor. Those…

The operad of moulds is realized in terms of an operational calculus of formal integrals (continuous formal power series). This leads to many simplifications and to the discovery of various suboperads. In particular, we prove a conjecture…

The main purpose of this paper is to study a concrete example of $\delta$-Koszul algebras, which is related to three questions raised by Green and Marcos in [3].

With the help of a computer, we prove the assertion made in the title.

We introduce the notion of homotopy inner products for any cyclic quadratic Koszul operad $\mathcal O$, generalizing the construction already known for the associative operad. This is done by defining a colored operad $\widehat{\mathcal…

This paper is a greatly expanded version of Section 9.11 in arXiv:1006.4343. A series of definitions and results illustrating the thesis in the title (where quasi-formality means vanishing of a certain kind of Massey multiplications in the…

This paper introduces the study of LG-quadratic quotients of exterior algebras, showing that they are Koszul, as in the commutative case. We construct an example of an LG-quadratic algebra that is not G-quadratic and another example that is…