Linking Lie groupoids and infinite-dimensional Lie theory

20.07.2018, 10:30  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Alexander Schmeding (TU Berlin)

Lie groupoids generalise Lie groups and the associated Lie
theory to regimes with symmetries which are not necessarily global in
nature (in the sense of being not induced by a Lie group action). It
is part of the mathematical folklore that to every Lie groupoid one
can associate an infinite-dimensional Lie group, the group of (global)
bisections. This construction yields an object which retains a
surprising amount of information on the groupoid and fits nicely into
the Lie theoretic framework for groupoids and infinite-dimensional
groups.
This talk is giving an introduction to the relation between Lie
groupoids and infinite-dimensional Lie groups. We will discuss some
main examples and implications of the construction in Lie theory and
representation theory. No prior knowledge about Lie groupoids and
infinite-dimensional Lie groups is assumed.