相关论文: Manin products, Koszul duality, Loday algebras and…
In the theory of binary quadratic operads, the white and black products of operads (called Manin products) play an important role. Given two such operads, the computation of either of their Manin products is a routine task. We present and…
In this thesis, we generalize the Koszul duality for associative algebras and operads to PROPs. The operads are algebraic objects that represent the operations with multiple inputs but only one output acting on a certain type of algebras. 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…
Algebraic structures with multiple copies of a given type of operations interrelated by various compatibility conditions have long being studied in mathematics and mathematical physics. They are broadly referred as linearly compatible,…
In this paper, we consider three types of operads: alternative, assosymmetric, and bicommutative. We prove that the Hadamard product of these operads with the Novikov operad coincides with their white Manin product. As an application, we…
We consider the notions of the replicators, including the duplicator and triplicator, of a binary operad. As in the closely related notions of di-Var-algebra and tri-Var-algebra in [14], they provide a general operadic definition for the…
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 $\hat{\mathcal O}$,…
The cup product in the cohomology of algebras over quadratic operads has been studied in the general setting of Koszul duality for operads. We study the cup product on the cohomology of n-ary totally associative algebras with an operation…
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 provides a general operadic definition for the notion of splitting the operations of algebraic structures. This construction is proved to be equivalent to some Manin products of operads and it is shown to be closely related to…
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…
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…
A quadratic algebra is a homogeneous algebra generated by its elements of degree 1. Manin has endowed the category of quadratic algebras with two tensor products. These structures have been adapted to operads by Ginsburg and Kapranov.…
For an associative algebra A we consider the pair "the Hochschild cochain complex C*(A,A) and the algebra A". There is a natural 2-colored operad which acts on this pair. We show that this operad is quasi-isomorphic to the singular chain…
We describe simple tricks to compute the Manin black products with the operads $\mathcal{A}ss$, $\mathcal{C}om$ and $pre\mathcal{L}ie$.
In this paper, we consider Novikov algebra with derivation and algebra obtained from its dual operad. It turns out that the obtained dual operad has a connection with bicommutative algebras. The motivation for this work comes from the white…
One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the developments of [3] and [2] by understanding the…
We introduce higher-order Massey products for algebras over algebraic operads. This extends the work of Fernando Muro on secondary ones. We study their basic properties and behavior with respect to morphisms of algebras and operads and give…
The purpose of this paper is two-fold. In Part 1 we introduce a new theory of operadic categories and their operads. This theory is, in our opinion, of an independent value. In Part 2 we use this new theory together with our previous…
We establish a duality between monads and monadic morphisms in any $(\infty,2)$-category and characterize monadic morphisms in a wide class of examples. This duality unifies several dualities between algebraic structures and their…