三变量多项式代数的过滤形变
Filtered deformations of three-variable polynomial algebras
- University of Waterloo（滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文分类三变量多项式环的所有过滤形变，并据此证明正特征代数闭域上具有有限维过滤且相伴分次环为三变量多项式环的代数满足多项式恒等式。
AI中文摘要：
我们分类了三变量多项式环的所有过滤形变。利用我们的刻画，我们回答了Etingof问题的一个特例，证明：若$F$是正特征代数闭域，且$A$是$F$-代数，具有由有限维子空间构成的过滤，其相伴分次环是三变量多项式环，则$A$满足一个多项式恒等式。
英文摘要：
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.
