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SUMMARY:Three dichotomies for connected unimodular Lie groups. - David Hum
 e (University of Oxford)
DTSTART:20191206T134500Z
DTEND:20191206T144500Z
UID:TALK134203@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:Using the Levi decomposition theorem\, Lie groups are usually 
 studied in two separate classes: semisimple and solvable. Both these class
 es further divide into two subclasses with very different behaviour: semis
 imple groups split into the rank 1 and higher rank cases\; while solvable 
 groups divide into those of polynomial growth and those of exponential gro
 wth.\n\nAmongst connected unimodular Lie groups\, let us say that G is "sm
 all" if it shares a cocompact subgroup with some direct product of a rank 
 one simple Lie group and a solvable Lie group with polynomial growth. Othe
 rwise\, we say G is "large". We present three strong dichotomies which dis
 tinguish "small" and "large" groups\; which are respectively algebraic\, c
 oarse geometric\, and local analytic in nature. As an application we will 
 show that Baumslag-Solitar groups admit a similar "small"/"large" dichotom
 y. This is part of a joint project with John Mackay and Romain Tessera.
LOCATION:CMS\, MR13
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