Yuri Bahturin, Memorial University of Newfoundland

Title: Generalizing classical correspondences between groups and Lie algebras

Abstract: There are different ways of building a Lie algebra of a group. One approach, due to A. I. Malcev, allows to introduce the structure of a Lie algebra on the (divisible nilpotent) group itself. Conversely, one can build a group on a (nilpotent) Lie algebra, using Baker-Campbell-Hausdorf formula. As a result, we have "hybrid" object, one author called them "groupalgebras" or "algebragroups". We observe that this approach works in a far wide setting of arbitrary nilpotent algebras. We also have new applications in the case of the classical Malcev correspondence. (This is joint work with A. Olshanskii.)