Related papers: On the Dong Property for a binary quadratic operad
A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all the tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma…
The associative operad is the quotient of the magmatic operad by the operad congruence identifying the two binary trees of degree $2$. We introduce here a generalization of the associative operad depending on a nonnegative integer $d$,…
This paper gives a systematic study of matching dialgebras corresponding to the operad $As^{(2)}$ in \cite{Zi} as the only Koszul self dual operad there other than the operads of associative algebras and Poisson algebras. The close…
We here both unify and generalize nonassociative structures on typed binary trees, that is to say plane binary trees which edges are decorated by elements of a set $\Omega$. We prove that we obtain such a structure, called an…
We introduce and study transposed Poisson conformal superalgebras, the $\mathbb Z_2$-graded conformal analogues of transposed Poisson algebras, as well as their noncommutative variants. We derive a family of identities forced by the…
We study quotients of the magmatic operad, that is the free nonsymmetric operad over one binary generator. In the linear setting, we show that the set of these quotients admits a lattice structure and we show an analog of the Grassmann…
The main feature of color Hom-algebras is that the identities defining the structures are twisted by even linear maps. The purpose of this paper is to introduce and give some constructions of admissible Hom-Novikov-Poisson color…
We investigate algebras with one operation. We study when these algebras form a monoidal category and analyze Koszulness and cyclicity of the corresponding operads. We also introduce a new kind of symmetry for operads, the dihedrality,…
Since its introduction by Loday in 1995 with motivation from algebraic K-theory, dendriform dialgebras have been studied quite extensively with connections to several areas in mathematics and physics. A few more similar structures have been…
We extend naturally the spectral triple which define noncommutative geometry (NCG) in order to incorporate supersymmetry and obtain supersymmetric Dirac operator D_M which acts on Minkowskian manifold. Inversely, we can consider the…
It is known that the operads of perm algebras and pre-Lie algebras are the Koszul dual each other and hence there is a Lie algebra structure on the tensor product of a perm algebra and a pre-Lie algebra. Conversely, we construct a special…
The associative operad is a central structure in operad theory, defined on the linear span of the set of permutations. We build two analogs of the associative operad on the linear span of the set of packed words which turn out to be…
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 use computational linear algebra and commutative algebra to study spaces of relations satisfied by quadrilinear operations. The relations are analogues of associativity in the sense that they are quadratic (every term involves two…
Let $\mathcal{M}$ be a von Neumann algebra, $\mathcal{I}$ a weak-operator dense ideal in $\mathcal{M}$, and $\Phi$ a unitarily invariant $\|\cdot\|$-dominating norm on $\mathcal{I}$. In this paper, we provide a necessary and sufficient…
We study from an algebraic and geometric viewpoint Hamiltonian operators which are sum of a non-degenerate first-order homogeneous operator and a Poisson tensor. In flat coordinates, also known as Darboux coordinates, these operators are…
Let P be a quadratic operad. We determine an associated operad ~P such that for any P-algebra A and any ~P-algebra B then the tensor product $A \otimes B$ is a P-algebra.
Livernet and Loday constructed a polarization of the nonsymmetric associative operad A with one operation into a symmetric operad SA with two operations (the Lie bracket and Jordan product), and defined a one-parameter deformation of SA…
The theme of this article is the algebraic combinatorics of leaf-labeled rooted binary trees and forests of such trees. The structure of a Hopf operad is defined on the vector spaces spanned by forests of leaf-labeled, rooted, binary trees.…
We introduce the notion of Leibniz conformal bialgebras, presenting a bialgebra theory for Leibniz conformal algebras as well as the conformal analogues of Leibniz bialgebras. They are equivalently characterized in terms of matched pairs…