Skip navigation
Veuillez utiliser cette adresse pour citer ce document : http://repositorio.unb.br/handle/10482/43775
Fichier(s) constituant ce document :
Il n'y a pas de fichiers associés à ce document.
Titre: Nil restricted Lie algebras of oscillating intermediate growth
Auteur(s): Petrogradsky, Victor
Assunto:: Álgebra
Lie, Álgebra de
P-grupos
Problema Kurosh
Date de publication: 15-déc-2021
Editeur: Elsevier
Référence bibliographique: PETROGRADSKY, Victor. Nil restricted Lie algebras of oscillating intermediate growth. Journal of Algebra, v. 588, p. 349-407, 2021. DOI: https://doi.org/10.1016/j.jalgebra.2021.09.003.
Abstract: The research is motivated by a construction of groups of oscillating growth by Kassabov and Pak [25] and a description of possible growth functions of finitely generated associative algebras by Bell and Zelmanov [9]. In this paper we address both, the question of possible growth functions in case of Lie algebras, and the Kurosh problem, because our examples of restricted Lie algebras have a nil p-mapping, which is an analogue of nillity for associative algebras or periodicity for groups. Namely, for any field of positive characteristic, we construct a family of 3-generated restricted Lie algebras of intermediate oscillating growth. We call them Phoenix algebras because, for infinitely many periods of time, the algebra is “almost dying” by having a quasi-linear growth, namely the lower Gelfand-Kirillov dimension is one, more precisely, the growth is of type , where , are constants. On the other hand, for infinitely many n the growth function has a rather fast intermediate behavior of type , λ being a constant determined by characteristic, for such periods the algebra is “resuscitating”. Moreover, the growth function is bounded and oscillating between these two types of behavior. These restricted Lie algebras have a nil p-mapping, thus addressing the Kurosh problem as well.
DOI: https://doi.org/10.1016/j.jalgebra.2021.09.003
metadata.dc.relation.publisherversion: https://www.sciencedirect.com/science/article/pii/S0021869321004324?via%3Dihub
Collection(s) :Artigos publicados em periódicos e afins

Affichage détaillé " class="statisticsLink btn btn-primary" href="/jspui/handle/10482/43775/statistics">



Tous les documents dans DSpace sont protégés par copyright, avec tous droits réservés.