Título:	Nil restricted Lie algebras of oscillating intermediate growth
Autor(es):	Petrogradsky, Victor
Assunto:	Álgebra Lie, Álgebra de P-grupos Problema Kurosh
Data de publicação:	15-Dez-2021
Editora:	Elsevier
Referência:	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
Versão da editora:	https://www.sciencedirect.com/science/article/pii/S0021869321004324?via%3Dihub
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