Nil restricted Lie algebras of oscillating intermediate growth

Petrogradsky, Victor

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Campo DC	Valor	Idioma
dc.contributor.author	Petrogradsky, Victor	-
dc.date.accessioned	2022-05-23T14:37:13Z	-
dc.date.available	2022-05-23T14:37:13Z	-
dc.date.issued	2021-12-15	-
dc.identifier.citation	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.	pt_BR
dc.identifier.uri	https://repositorio.unb.br/handle/10482/43775	-
dc.language.iso	Inglês	pt_BR
dc.publisher	Elsevier	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	Nil restricted Lie algebras of oscillating intermediate growth	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Álgebra	pt_BR
dc.subject.keyword	Lie, Álgebra de	pt_BR
dc.subject.keyword	P-grupos	pt_BR
dc.subject.keyword	Problema Kurosh	pt_BR
dc.identifier.doi	https://doi.org/10.1016/j.jalgebra.2021.09.003	pt_BR
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S0021869321004324?via%3Dihub	pt_BR
dc.description.abstract1	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.	pt_BR
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