相关论文: An operational calculus for the Mould operad

In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.

There are basically two interesting breeds of $E_2$ operads, those that detect loop spaces and those that solve Deligne's conjecture. The former deformation retract to Milgram's space obtained by gluing together permutahedra at their faces.…

Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no general way to transport spectral invariants in a functorial…

We propose to use Church encodings in typed lambda-calculi as the basis for an automata-theoretic counterpart of implicit computational complexity, in the same way that monadic second-order logic provides a counterpart to descriptive…

We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…

We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial…

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 article is studied the construction of free operads functor, for the symmetric and non-symmetric case. In order to do this, the operads are seen as monoids on the differential graded modules category. In the last part we show some…

The overall aim of this paper is to define a structure of graph operads, thus generalizing the celebrated pre-Lie operad on rooted trees. More precisely, we define two operads on multigraphs, and exhibit a non trivial link between them and…

For a directed polytope, we construct a colored operad whose Poincare-Hilbert series encodes certain operations on the cellular complex of the polytope. We conjecture that for a class of short polytopes the constructed operads are Koszul…

We introduce a systematic method for constructing set-theoretic operads via iterated application of the power set functor, and use it to uncover a hierarchy connecting several classical operads. Starting from the permutative operad, the…

We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…

This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…

We introduce a functorial construction $\mathsf{C}$ which takes unitary magmas $\mathcal{M}$ as input and produces operads. The obtained operads involve configurations of chords labeled by elements of $\mathcal{M}$, called…

Using the combinatorial species setting, we propose two new operad structures on multigraphs and on pointed oriented multigraphs. The former can be considered as a canonical operad on multigraphs, directly generalizing the…

A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and…

We endow categories of non-symmetric operads with natural model structures. We work with no restriction on our operads and only assume the usual hypotheses for model categories with a symmetric monoidal structure. We also study categories…

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.

Circuit algebras are a symmetric analogue of Jones's planar algebras introduced to study finite-type invariants of virtual knotted objects. Circuit algebra structures appear, in different forms, across mathematics. This paper provides a…

This paper shows that generalizations of operads equipped with their respective bar/cobar dualities are related by a six operations formalism analogous to that of classical contexts in algebraic geometry. As a consequence of our…