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The Nash-Moser Theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras | | Alfredo Brega
; Leandro Cagliero
; Augusto Chaves Ochoa
; | | Date: |
4 Dec 2015 | | Abstract: | This paper consists of two parts. In the first one we give an elementary
proof of a finite dimensional version of the Nash-Moser theorem for exact
sequences of R. Hamilton. In the second part, we apply this theorem to the
context of deformations of Lie algebras and we discuss some aspects of the
scope of this theorem in connection with the polynomial ideal associated to the
variety of nilpotent Lie algebras. We discuss degenerations and rigidity in the
variety of $k$-step nilpotent Lie algebras of dimension $n$ with $nle7$
recovering some known results. As a new result, we obtain rigid Lie algebras
and rigid curves in the variety of 3-step nilpotent Lie algebras of dimension
$7$. Finally we point out some possible errors in the bibliography related to
the classification and deformations of these Lie algebras. | | Source: | arXiv, 1512.1514 | | Services: | Forum | Review | PDF | Favorites | |
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