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SUMMARY:Jonas Deré (KU Leuven Kulak)
DTSTART:20220223T160000Z
DTEND:20220223T170000Z
DTSTAMP:20260423T021218Z
UID:VSGS/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/43/">Si
 mply transitive NIL-affine actions of solvable Lie groups</a>\nby Jonas De
 ré (KU Leuven Kulak) as part of Virtual seminar on geometry with symmetri
 es\n\n\nAbstract\nAlthough not every $1$-connected solvable Lie group $G$ 
 admits a simply transitive action via affine maps on $\\mathbb{R}^n$\, it 
 is known that such an action exists if one replaces $\\mathbb{R}^n$ by a s
 uitable nilpotent Lie group $N$\, depending on $G$. However\, not much is 
 known about which pairs of Lie groups $(G\,N)$ admit such an action\, wher
 e ideally you only need information about the Lie algebras corresponding t
 o $G$ and $N$. The most-studied case is when $G$ is assumed to be nilpoten
 t\, then the existence of a simply transitive action is related to the not
 ion of complete pre-Lie algebra structures.\n\nIn recent work with Marcos 
 Origlia\, we showed how this problem is related to the semisimple splittin
 g of the Lie algebra corresponding to $G$. Our characterization not only a
 llows us to check whether a given action is simply transitive\, but also w
 hether a simply transitive action exists given the Lie groups $G$ and $N$.
  As a consequence\, we list the possibilities for such actions up to dimen
 sion $4$.\n
LOCATION:https://researchseminars.org/talk/VSGS/43/
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