On growth of Lie algebras, generalized partitions, and analytic functions
type: Item
instance of: scholarly article
title: On growth of Lie algebras, generalized partitions, and analytic functions
zbMATH Open document ID: 0970.17003
DOI: 10.1016/S0012-365X(99)00271-X
published in: Discrete Mathematics
publication date: 2001-10-14T00:00:00Z
review text: The article is a review of results concerning two different types of growth of Lie algebras that lead to some combinatorial problems. The first of them is the growth of finitely generated Lie algebras that leads to a study of generalized partitions. Some results on asymptotics for generalized partitions are given in the paper. A main application is an asymptotical result for the growth of free polynilpotent finitely generated Lie algebras. As a corollary, the author specifies the asymptotic growth of lower central series ranks for free polynilpotent finitely generated groups. The second aspect discussed in the article is a codimensional growth for varieties of Lie algebras. In this connection the author considers some exponential generating functions called complexity functions. Those functions are entire functions of a complex variable. The author computes complexity functions for some varieties. The growth of a complexity function for an arbitrary polynilpotent variety is evaluated. As results the asymptotics of the codimensional growth of a polynilpotent variety of Lie algebras and an upper bound for the growth of an arbitrary nontrivial variety of Lie algebras are obtained. No proofs are included.
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 16R10
zbMATH DE Number: 1453360
zbMATH Keywords: Lie algebra
zbMATH Keywords: growth of finitely generated algebra
zbMATH Keywords: generalized partitions
zbMATH Keywords: codimension growth
author: Victor Petrogradsky
reviewed by: Boris Vernikov
MaRDI profile type: Publication
full work available at URL: s0012-365x(99)00271-x
OpenAlex ID: W2041116857
description: scientific article; zbMATH DE number 1453360