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arXiv · 1602.06480

A PI degree theorem for quantum deformations

Pavel Etingof
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Abstract

Let $F$ be an algebraically closed field. We show that if a quantum formal deformation $A$ of a commutative domain $A_0$ over $F$ is a PI algebra, then $A$ is commutative if ${\rm char}(F)=0$, and has PI degree a power of $p$ if ${\rm char}(F)=p>0$. This implies the same result for filtered deformations (i.e., filtered algebras $A$ such that ${\rm gr}(A)=A_0$).

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Pavel Etingof. 2016-02-21. A PI degree theorem for quantum deformations. https://arxiv.org/abs/1602.06480

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