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arXiv · 2606.29060

The PI property of skew PBW extensions

James Gómez·Claudia Gallego
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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.

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James Gómez, Claudia Gallego. 2026-06-27. The PI property of skew PBW extensions. https://arxiv.org/abs/2606.29060

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