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Intermediate Growth in Lie Algebras and Their Enveloping Algebras

✍ Scribed by V.M. Petrogradsky

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
276 KB
Volume
179
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper a series of dimensions is suggested which includes as first terms dimension of a vector space, Gelfand᎐Kirillov dimension, and superdimension. In terms of these dimensions we describe the change of a growth in transition from a Lie algebra to its universal enveloping algebra. Also, we find the growth of free polynilpotent finitely generated Lie algebras; as an application we specify those algebras with rational Hilbert᎐Poincare series. As a corollary we find an asymp-totic growth of lower central series ranks for free polynilpotent finitely generated groups.

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