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arXiv · 2609.06710

Filtered deformations of three-variable polynomial algebras

Jason Bell·Boris Li
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Abstract

We classify all filtered deformations of polynomial rings in three variables. We use our characterization to answer a special case of a question of Etingof by showing that if $F$ is an algebraically closed field of positive characteristic and $A$ is an $F$-algebra with a filtration by finite dimensional subspaces whose associated graded ring is a polynomial ring in three variables then $A$ satisfies a polynomial identity.

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Jason Bell, Boris Li. 2026-09-06. Filtered deformations of three-variable polynomial algebras. https://arxiv.org/abs/2609.06710

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