On Nichols algebras of infinite rank with finite Gelfand-Kirillov dimension

TL;DR

This paper classifies certain infinite-dimensional Nichols algebras with finite Gelfand-Kirillov dimension, providing explicit examples for each natural number dimension, advancing understanding of their structure and classification.

Contribution

It offers a classification of infinite-dimensional Nichols algebras from decomposable braided vector spaces with finite Gelfand-Kirillov dimension, including explicit examples for all natural numbers.

Findings

Classified infinite-dimensional Nichols algebras with finite Gelfand-Kirillov dimension.

Constructed examples with Gelfand-Kirillov dimension equal to any natural number.

Identified structural conditions for these Nichols algebras.

Abstract

We classify infinite-dimensional decomposable braided vector spaces arising from abelian groups whose components are either points or blocks such that the corresponding Nichols algebras have finite Gelfand-Kirillov dimension. In particular we exhibit examples with $\operatorname{GKdim} = n$ for any natural number $n$.