Related papers: Operad profiles of Nijenhuis structures
This paper is the second in a series dedicated to the operadic study of Nijenhuis structures, focusing on Nijenhuis Lie algebras and Nijenhuis geometry. We introduce the concept of homotopy Nijenhuis Lie algebras and establish that the…
This paper is the first in a series of works devoted to an operadic study of Nijenhuis structures, focusing on Nijenhuis associative algebras. We introduce the concept of homotopy Nijenhuis associative algebras and demonstrate that the…
The goal of this paper is to prove a Koszul duality result for E_n-operads in differential graded modules over a ring. The case of an E_1-operad, which is equivalent to the associative operad, is classical. For n>1, the homology of an…
We find a minimal differential graded (dg) operad whose generic representations in $R^n$ are in one-to-one correspondence with formal germs of those endomorphisms of the tangent bundle to $R^n$ which satisfy the Nijenhuis integrability…
Nijenhuis operators are very useful in the deformation theory of algebras. In this paper, we introduce a new cohomology theory related to deformation of Nijenhuis algebra morphisms, this notion involves simultaneous deformation of two…
This paper studies the Nijenhuis operator on Hom-Leibniz conformal algebra, defining their representations and cohomologies. We determine the cohomologies for both Hom-Leibniz conformal algebra and Nijenhuis operators on Hom-Leibniz…
We study the operad structure on the homology of moduli spaces of pointed rooted trees of $d$-dimensional projective spaces, introduced by Chen, Gibney and Krashen a couple of decades ago. We describe this operad by generators and…
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…
We extend bar-cobar duality, defined for operads of chain complexes by Getzler and Jones, to operads of spectra in the sense of stable homotopy theory. Our main result is the existence of a Quillen equivalence between the category of…
In this paper, we introduce the notion of Koszul-Vinberg-Nijenhuis structures on a left-symmetric algebroid as analogues of Poisson-Nijenhuis structures on a Lie algebroid, and show that a Koszul-Vinberg-Nijenhuis structure gives rise to a…
We describe a cooperad structure on the simplicial bar construction on a reduced operad of based spaces or spectra and, dually, an operad structure on the cobar construction on a cooperad. We also show that if the homology of the original…
The goal of this article is to make explicit a structured complex whose homology computes the cohomology of the p-profinite completion of the n-fold loop space of a sphere of dimension d=n-m<n. This complex is defined purely algebraically,…
We give a new short proof that the wheeled operad of unimodular Lie algebras is Koszul and use this to explicitly construct its minimal resolution. A representation of this resolution in a finite dimensional vector space V we call a…
We define a construction on operads which yields a new description of the minimal model. The construction also allows us to define algebraic structures on the homology of chain complexes with homologously trivial operad algebra structures,…
Curved algebras are a generalization of differential graded algebras which have found numerous applications recently. The goal of this foundational article is to introduce the notion of a curved operad, and to develop the operadic calculus…
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…
We study algebras with a distributive law and the Koszulness of associated operads. As a corollary of our theory we prove that the homology operad of the little cubes operad is Koszul, the result which was originally proven by E. Getzler…
In this paper we describe operads encoding two different kinds of compatibility of algebraic structures. We show that there exist decompositions of these in terms of black and white products and we prove that they are Koszul for a large…
We study two closely related operads: the Gelfand-Dorfman operad GD and the Conformal Lie Operad CLie. The latter is the operad governing the Lie conformal algebra structure. We prove Koszulity of the Conformal Lie operad using the Groebner…
We show that the Koszul dual of an E_n-operad in spectra is O(n)-equivariantly equivalent to its n-fold desuspension. To this purpose we introduce a new O(n)-operad of Euclidean spaces R_n, the barycentric operad, that is fibred over…