Agust'in Garrone

activity

20242026

collaborators

5 papers

math.DG2026

On centerless unimodular contact Lie algebras

AgustÃn Garrone

We provide an elementary proof that, in a (transversely) unimodular contact Lie algebra, the adjoint action of the Reeb vector is nilpotent except when the Lie algebra is isomorphi…

math.DG2026

1-Lefschetz contact solvmanifolds

AdriÃ¡n Andrada, AgustÃn Garrone

We study the contact Lefschetz condition on compact contact solvmanifolds, as introduced by B.\ Cappelletti-Montano, A.\ De Nicola and I.\ Yudin. We seek to fill the gap in the lit…

math.DG2025

Symplectic solvmanifolds not satisfying the hard-Lefschetz condition

AdriÃ¡n Andrada, AgustÃn Garrone

For Lie groups $G$ of the form $G = R^{k} ⋉_{I ¨} R^{m}$ , with $k + m$ even, a result of H. Kasuya shows that if the action $I ¨ : R^{k} \to Aut (R^{m})$ is semisimple then any…

math.DG2025

Hypercomplex structures on special linear groups

AdriÃ¡n Andrada, AgustÃn Garrone, Alejandro Tolcachier

The purpose of this article is twofold. First, we prove that the $8$ -dimensional Lie group $SL (3, R)$ does not admit a left-invariant hypercomplex structure.…

math.DG2024

Construction of symplectic solvmanifolds satisfying the hard-Lefschetz condition

AdriÃ¡n Andrada, AgustÃn Garrone

A compact symplectic manifold $(M, I ¨ )$ is said to satisfy the hard-Lefschetz condition if it is possible to develop an analogue of Hodge theory for $(M, I ¨ )$ . This loosely means t…