The PI property of skew PBW extensions

James Gómez; Claudia Gallego

The PI property of skew PBW extensions

Rings and Algebras 2026-06-27 v1

Authors: James Gómez , Claudia Gallego

Abstract

In this article we study the polynomial identity (PI) property of skew PBW extensions. We show that every bijective skew PBW extension over a prime PI-algebra has nontrivial center. This fact allows us to determine, from the known description of the center in several classes of examples, whether such extensions satisfy a polynomial identity. Furthermore, building on results of Brown and Zhang \cite{BrownZhang2022}, we investigate the PI property of certain $\K$ -algebras over fields of positive characteristic.

Keywords

skew PBW extensions polynomial identity property prime PI-algebra center positive characteristic

Cite

@article{arxiv.2606.29060,
  title  = {The PI property of skew PBW extensions},
  author = {James Gómez and Claudia Gallego},
  journal= {arXiv preprint arXiv:2606.29060},
  year   = {2026}
}