Colloquium: Tuesday, December 8, 2pm. Speaker: Andrei Minchenko (Weizmann). Title: Linear differential algebraic groups and central extensions.
At the most basic level, a linear differential algebraic group (LDAG) is a group of matrices whose entries are functions satisfying a fixed set of polynomial differential equations. These groups are important for applications to differential Galois theory. Although LDAGs are infinite dimensional, they share many good properties with algebraic groups. In general, LDAGs do not have finite subnormal series with simple quotients. However, as was shown by Cassidy and Singer, there is a subnormal series whose non-commutative quotients are central extensions of simple LDAGs. It turns out that these extensions are isomorphisms. We will also see an interesting application of the related work to Chevalley groups.