Conference abstracts

Session S03 - Hopf Algebras

July 26, 17:30 ~ 17:55

## Non-associative exponentials and the Baker–Campbell–Hausdorff formula

### Jacob Mostovoy

### CINVESTAV-IPN, Mexico - jacob@math.cinvestav.mx

An exponential map is a power series in one variable that sends the set of primitive elements in a complete Hopf algebra to the set of its group-like elements, and whose linear term has coefficient 1. While the exponential map is unique in the associative setting, in the non-associative case there are infinitely many exponential maps.

In this talk I will describe the set of all non-associative exponential maps as a torsor for a certain residually nilpotent group. I will also talk about the problem of constructing the non-associative version of the Dynkin form of the Baker-Campbell-Hausdorff formula; that is, expressing $\log(\exp(x) \exp(y))$, where $x$ and $y$ are non-associative variables, in terms of the Shestakov-Umirbaev primitive operations.

Joint work with J.M. Pérez Izquierdo (Universidad de la Rioja, España) and I.P. Shestakov (Universidade de São Paulo, Brasil).