Related papers: Signaletic operads

We introduce here the notion of Koszul duality for monoids in the monoidal category of species with respect to the ordinary product. To each Koszul monoid we associate a class of Koszul algebras in the sense of Priddy, by taking the…

We introduce a functor ${\sf As}$ from the category of posets to the category of nonsymmetric binary and quadratic operads, establishing a new connection between these two categories. Each operad obtained by the construction ${\sf As}$…

We extend the Koszul duality theory of associative algebras to algebras over an operad. Recall that in the classical case, this Koszul duality theory relies on an important chain complex: the Koszul complex. We show that the cotangent…

The present article exploits the fact that permutads (aka shuffle algebras) are algebras over a terminal operad in a certain operadic category Per. In the first, classical part we formulate and prove a claim envisaged by Loday and Ronco…

This paper studies the operad of linearly compatible di-algebras, denoted by $As^{2}$, which is a nonsymmetric operad encoding the algebras with two binary operations that satisfy individual and sum associativity conditions. We also prove…

We study colored generalizations of the symmetric algebra and its Koszul dual, the exterior algebra. The symmetric group $\mathfrak{S}_n$ acts on the multilinear components of these algebras. While $\mathfrak{S}_n$ acts trivially on the…

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 study the operad $n\text{-}Lie_d$, whose algebras are graded $n$-Lie algebras with degree $d$ $n$-arity operations, which were introduced in Nambu mechanics and later studied in the algebraic setting with Filippov. We compute the Koszul…

We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras on a fixed space M. his allows us to describe a notion of prefactorization algebra up to…

We consider the Knizhnik-Zamolodchikov and dynamical operators, both differential and difference, in the context of the $(\mathfrak{gl}_{k}, \mathfrak{gl}_{n})$-duality for the space of polynomials in $kn$ anticommuting variables. We show…

We consider partitions of a set with $r$ elements ordered by refinement. We consider the simplicial complex $\bar{K}(r)$ formed by chains of partitions which starts at the smallest element and ends at the largest element of the partition…

This is a copy of the article by the same authors published in Duke Math. J. (1994).

We consider rational power series over an alphabet $\Sigma$ with coefficients in a ordered commutative semiring $K$ and characterize them as the free ordered $K$-semialgebras in various classes of ordered $K$-semialgebras equipped with a…

We will extend the classical derived bracket construction to any algebra over a binary quadratic operad. We will show that the derived product construction is a functor given by the Manin white product with the operad of permutation…

Prestacks are algebro-geometric objects whose defining relations are far from quadratic. Indeed, they are cubic and quartic, and moreover inhomogeneous. Similarly, a morphism of $P$-algebras for a (nonsymmetric) Koszul operad $P$ has…

Motivated by numerous examples in the literature, we state a conjecture on the Hilbert series of Koszul symmetric operads generated by one element of arity $2$. We prove this conjecture for all Koszul symmetric set-operads generated by one…

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…

We generalize the construction of multitildes in the aim to provide multitilde operators for regular languages. We show that the underliying algebraic structure involves the action of some operads. An operad is an algebraic structure that…

Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…

We describe the Koszul dual of two quadratic operads on planar forests introduced to study the infinitesimal Hopf algebra of planar rooted trees and prove that these operads are Koszul.