51 citations · 122 across the 18 of their papers we have counts for
19 papers
Complex structures on two-step nilpotent Lie groups
Maria Laura Barberis
We give a characterization of the -step nilpotent Lie algebras whose corresponding Lie groups admit a left invariant complex structure. This is done by considering separately th…
Holonomy of the Obata connection on 2-step hypercomplex nilmanifolds
Adrián Andrada, María Laura Barberis, Beatrice Brienza
We study the holonomy of the Obata connection on 2-step hypercomplex nilmanifolds. By explicitly computing the curvature tensor, we determine the conditions under which the Obata c…
Almost abelian complex nilmanifolds
Adrián Andrada, Romina M. Arroyo, María L. Barberis +2
We show that a complex structure on a nilpotent almost abelian real Lie algebra is unique if it exists. As a consequence, we get full control over the cohomology and deformations o…
Classification of almost abelian Lie groups admitting left-invariant complex or symplectic structures
Romina M. Arroyo, María L. Barberis, Verónica S. Diaz +2
We classify the almost abelian Lie algebras admitting complex or symplectic structures. The matrix $A\in M(2n-1,\mathbb R )…
Applications of the quaternionic Jordan form to hypercomplex geometry
Adrián Andrada, María Laura Barberis
We apply the quaternionic Jordan form to classify the hypercomplex nilpotent almost abelian Lie algebras in all dimensions and to carry out the complete classification of 12-dimens…
Hypercomplex almost abelian solvmanifolds
Adrián Andrada, María Laura Barberis
We give a characterization of almost abelian Lie groups carrying left invariant hypercomplex structures and we show that the corresponding Obata connection is always flat. We deter…