Alladi Ramakrishnan Hall

The Kneser-Tits problem

Maneesh Thakur

ISI, Delhi

Let G be a semisimple, simply connected algebraic group, defined over a
field K. Let G(K) denote the group of K-rational points of G. Assume that G is
simple and isotropic over K. Let G(K)+ be the (normal) subgroup of G(K) generated by
the K-rational points of the unipotent radicals of K-parabolics of G. The
Kneser-Tits problem asks if G(K)=G(K)+. When K is perfect, this is equivalent to the
question if G(K) is simple modulo its center. We will discuss this problem along
with some other related notions for algebraic groups.