Nested Pre-Lie Operads and Infinitesimal Hopf Algebras

Abstract: 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 combinatorial species based on polynomial functions. Finally, we show that the NPL-operad on cycles induces an infinitesimal bialgebra structure (in the sense of Loday-Ronco) on the tensor algebra T(V), together with a pre-Lie algebra structure using a construction from Aguiar. This is joint work with Dominique Manchon, Hedi Regeiba, and Imen Rjaiba.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar