When the Lie group exponential is bad

21.06.2024, 11:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Alexander Schmeding (Trondheim) via ZOOM

From finite dimensional Lie theory, it is well known that the Lie group exponential yields a local diffeomorphism from the Lie algebra onto a unit neighborhood of the Lie group. These exponential coordinates are useful tools to understand the interplay between Lie algebra and Lie group. It is well known that this correspondence breaks down in infinite-dimensional Lie theory. Beyond Banach spaces, the Lie group exponential is in general not a local diffeomorphism. For these non-locally exponential Lie groups the Lie group exponential becomes much more restricted. In this talk we will revisit some of the classical examples of the breakdown of the exponential (e.g. the diffeomorphism group). It turns out that in many known examples this defect can be traced to properties of flows of vector fields. Time permitting, we will show some new results for non-local exponentiality of semidirect products of Lie groups.

This is joint work with R. Dahmen and K.-H. Neeb


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