Scale for codimension growth of Poisson PI-algebras

TL;DR

This paper establishes a scale for the codimension growth of Poisson PI-algebras, extending previous results from associative and Lie PI-algebras, and explores growth bounds and behaviors using advanced mathematical techniques.

Contribution

It introduces a new scale for the codimension growth of Poisson PI-algebras satisfying Lie identities, connecting it with exponential and factorial growth functions.

Findings

The scale stratifies the codimension growth of Poisson PI-algebras.

A new bound on Lie PI-algebra codimension growth is derived.

Analysis of very fast codimension growth in certain Poisson algebras.

Abstract

A.Regev proved that the codimension growth of an associative PI-algebra is at most exponential. The author established a scale for the codimension growth of Lie PI-algebras, which includes a series of functions between exponential and factorial functions. We prove that the same scale stratifies the ordinary codimension growth of Poisson PI-algebras satisfying Lie identical relations. As a byproduct, we obtain a new bound on the codimension growth of Lie PI-algebras in terms of complexity functions. We also study very fast codimension growth of some Poisson algebras without Lie identities. We essentially use techniques of exponential generating functions and growth of respective fast growing entire functions.