Pseudo-K\'ahler and hypersymplectic structures on semidirect products
| Autor: | Conti, Diego, Gil-García, Alejandro |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study left-invariant pseudo-K\"ahler 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-K\"ahler 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 Comment: 27 pages |
| Databáze: | arXiv |
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