8 papers
-step nilpotent symplectic Lie algebras associated with graphs
Josefina Barrionuevo, Paulo Tirao, Sonia Vera
We construct families of -step nilpotent symplectic Lie algebras associated with graphs, extending the construction given in [Pouseele-Tirao, JPAA 213 (2009)] for the 2-step cas…
On the rigidity of k-step nilpotent graph Lie algebras
Josefina Barrionuevo, Paulo Tirao
We thoroughly explore the class of k-step nilpotent Lie algebras associated with a simple graph looking for k-step nilpotent Lie algebras which are rigid in the variety of at most…
Rigid 2-step graph Lie algebras
Josefina Barrionuevo, Paulo Tirao
We characterize those graphs which correspond to a rigid 2-step nilpotent Lie algebra in the variety of at most 2-step nilpotent Lie algebras.
Deformations and rigidity in varieties of Lie algebras
Josefina Barrionuevo, Paulo Tirao
We present a novel construction of linear deformations for Lie algebras and use it to prove the non-rigidity of several classes of Lie algebras in different varieties. We consider…
An elementary approach to certain bilinear estimates
Jose A. Barrionuevo, Jarod Hart, Lucas Oliveira
We prove L2 x L2 to weak L1 estimates for some novel bilinear maximal operators of Kakeya and lacunary type thus extending to this setting, the works of Cordoba and of Nagel, Stein…
A Note on Maximal Averages in the Plane
Jose A. Barrionuevo, Lucas Oliveira
Using variants of the TT* method we give a self-contained proof of the result of Alfonseca, Soria and Vargas on maximal operators on arbitrary directions in $\rr^2$. We also give a…