Fine structures inside the PreLie operad

نویسندگان

  • Frédéric Chapoton
  • F. Chapoton
چکیده

This article aims at a detailed analysis of the PreLie operad. We obtain a more concrete description of the relationship between the anticyclic structure of PreLie and the generators of PreLie as a Lie-module, which was known before only at the level of characters. Building on this, we obtain an inclusion of the cyclic Lie module in the PreLie operad. We conjecture that the image of this inclusion generates an interesting free sub-operad.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Rooted trees and an exponential-like series

This paper deals with a group of generalized power series associated to any augmented operad, focusing on the case of the PreLie operad. The solution of flow equations using the pre-Lie structure on vector fields on an affine space gives rise to an interesting element of this group. 0 Introduction This paper is composed of three main ingredients: the first is the definition of a group of power ...

متن کامل

Derived bracket construction and Manin products

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 algebras. As an application, we will show that the operad of prePoisson algebras is isomorphic to Manin black product of the Poisson operad with the preLie operad. ...

متن کامل

Free pre-Lie algebras are free as Lie algebras

We prove that free pre-Lie algebras, when considered as Lie algebras, are free. Working in the category of S-modules, we define a natural filtration on the space of generators. We also relate the symmetric group action on generators with the structure of the anticyclic PreLie operad.

متن کامل

$omega$-Operads of coendomorphisms and fractal $omega$-operads for higher structures

     In this article we introduce the notion of textit{Fractal $omega$-operad} emerging from  a natural $omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $omega$-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural $omeg...

متن کامل

An operadic approach to deformation quantization of compatible Poisson brackets

An analogue of the Livernet–Loday operad for two compatible brackets, which is a flat deformation of the bi-Hamiltonian operad is constructed. The Livernet–Loday operad can be used to define ⋆-products and deformation quantization for Poisson structures. The constructed operad is used in the same way, introducing a definition of operadic deformation quantization of compatible Poisson structures...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017