Algebra Seminar: Garner -- The Campbell-Baker-Hausdorff adjunction

Richard Garner (Macquarie University) 

Friday 30 September, 12-1pm, Place: Carslaw 375 

The Campbell-Baker-Hausdorff adjunction.

The Lie algebra associated to a Lie group G encodes the
first-order infinitesimal structure of G near the identity; on the other
hand, the formal group law associated to G is a collection of formal
power series which encode all finite-order infinitesimal behaviour. One
extracts the formal group law from the Lie group by Taylor expanding the
multiplication with respect to some chart around the identity;
alternatively, one may build the formal group law from the Lie algebra
by applying the Campbell-Baker-Hausdorff (CBH) formula, which expresses
the group multiplication power series near the identity purely in terms
of iterated Lie brackets. There are a number of ways of deriving the CBH
formula, some geometric and some algebraic in nature. The aim of this
talk is to describe a categorical approach drawing on synthetic
differential geometry.