On growth of metabelian Lie algebras
Dilber Kocak

TL;DR
This paper constructs finitely presented metabelian Lie algebras with intermediate growth rates, expanding understanding of algebraic growth behaviors and providing explicit examples with growth types between polynomial and exponential.
Contribution
It introduces a method to produce finitely presented metabelian Lie algebras with specific intermediate growth rates, filling a gap in the classification of algebraic growth.
Findings
Explicit examples of finitely presented metabelian Lie algebras with intermediate growth.
Calculation of growth types for these algebras.
Demonstration of growth rates of the form e^{n^{d/(d+1)}} for integer d 1.
Abstract
For any integer we construct examples of finitely presented algebras with intermediate growth of type . We produce these examples by computing the growth types of some finitely presented metabelian Lie algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Meromorphic and Entire Functions
