3:00 p.m., Friday (October 15, 2004)
Math Annex 1100
Department of Mathematics, UBC
Cayley maps for algebraic groups
The exponential map plays an important role in Lie theory; it allows one to
linearize a Lie group in the neighborhood of the identity element, thus
reducing many questions about Lie groups to (more tractable) questions about
Lie algebras. Unfortunately (at least for an algebraic geometer), the
exponential map is not algebraic; it is given by an infinite series and thus
cannot be defined in the setting of algebraic groups.
The next best thing is to linearize the conjugation action of G on itself
in a Zariski neighborhood of the identity element. For special orthogonal
groups SO_n this is done by the classical Cayley map, which has been used
in place of the exponential map in many applications. In the 1980s D. Luna
asked which other simple algebraic groups admit a "Cayley map". In this talk,
I will discuss the background of this problem and a recent solution, obtained
jointly with N. Lemire and V.L. Popov.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).