30 nov 2023 -- 15:00
Geometry in Como (hybrid)
Room V2.10, Via Valleggio 11, Como
Abstract.
We study left-invariant pseudo-Kähler and hypersymplectic structures on semidirect products $G\rtimes H$; we work at the level of the Lie algebra $\mathfrak{g}\rtimes\mathfrak{h}$. In particular we consider the structures induced on $\mathfrak{g}\rtimes\mathfrak{h}$ by existing pseudo-Kähler structures on $\mathfrak{g}$ and $\mathfrak{h}$; we classify all semidirect products of this type with $\mathfrak{g}$ of dimension $4$ and $\mathfrak{h}=\mathbb{R}^2$. In the hypersymplectic setting, we consider a more general construction on semidirect products. We construct new $2$-step nilpotent hypersymplectic Lie algebras; to our knowledge, these are the first such examples whose underlying complex structure is not abelian. This is a joint work with Diego Conti (https://arxiv.org/abs/2310.20660).