26/10/2017, 14.30 hs, aula 27 FaMAF

Rigidity of the k-steps nilpotent Lie algebras through the Nash-Moser theorem

Speaker: Augusto Chavez

Abstract: Given the set of k-step nilpotent Lie algebras of dimension n, we associate an algebraic set N_{n, k} for them. We apply the Nash-Moser theorem to exact sequences of R. Hamilton in the context of rigidity in the set N_{n, k}.
Given a k-step nilpotent Lie algebra of dimension n, we will discuss some aspects of a certain vector space H^{2} _{k-nil} (g, g), which gives us information about the rigidity of g in N_{n, k}. We will give some examples of rigid Lie algebras in N_{n,k}. When k = 2, we will present some more criteria on rigidity in N_ {n, 2}.