Leibniz Algebras of Maximum Length and Their Applications

Elisa Cañate - UFAL

Resumo: Non associative algebras appear at the beginning of the twentieth century as a consequence of the development of quantum mechanics. Pascual Jordan, John von Neumann and Eugene Wigner were the first researchers in introducing theses kinds of algebras in 1934 and then, Jean-Louis Loday introduced the Leibniz algebras in 1993.
Thanks to Levi-Malcev's theorem, the nilpotent Lie algebras have played an important role in mathematics over the last years, either in the classification theory or in geometrical and analytical applications. In Leibniz algebras, the analogue of Levi-Malcev's theorem was proved by Barnes recently, thus nilpotent algebras still play a central role.
The aim of this talk is to show the study of some nilpotent Leibniz algebras and some of their applications, as geometrical applications or physical applications . Since the description of nilpotent algebras seen to be unsolvable, we reduce our discussion to the nilpotent family with some restriction on their nilindex and their gradation. More precisely, we study the p-filiform Leibniz algebras whose gradation is of maximum length. This family is very interesting since it has a close relationship with their physical applications, making easier the cohomology study for instance, the space of derivation or the first space of cohomology.

Local: Sala B do IM-Novo
Data: 27/09/13(Sexta-Feira)
Hora: 10:00