Yannic Vargas (CUNEF University Madrid)
We present an introduction to pre-Lie algebras, an algebraic structure closely related to Lie algebras. From a combinatorial perspective, pre-Lie algebras are connected to the notion of insertion of objects of a given nature into one another. In recent years, pre-Lie algebras have found numerous applications in algebra, combinatorics, quantum field theory, and numerical analysis.
To better understand the nature of pre-Lie algebras, we employ the framework of species, a categorification of the concept of generating functions. This perspective allows us to describe, in a combinatorial way, several algebraic properties of pre-Lie algebras. In particular, we present a “pre-Lie-like” notion of symmetric operads, called Nested Pre-Lie operads (NPL for short). After giving several examples of NPL operads, we explain how to construct NPL-algebras, in the same way algebraic structures emerge from operads by considering algebras over operads.
To do so, we use a new variant of species based on polynomial functions. This is joint work with Dominique Manchon, Hedi Regeiba, and Imen Rjaiba.
For more information and log in details please contact Christian Molle.
