LAUSR

Let $\Bbbk$ be a field of characteristic zero. For any positive integer $n$ and any scalar $a\in \Bbbk$ , we construct a family of Artin–Schelter regular algebras $R(n,a)$ , which are quantizations of Poisson structures on $\Bbbk [x_{0},\ldots ,x_{n}]$ . This generalizes an example given by Pym when $n=3$ . For a particular choice of the parameter $a$ we obtain new examples of Calabi–Yau algebras when $n\geqslant 4$ . We also study the ring theoretic properties of the algebras $R(n,a)$ . We show that the point modules of $R(n,a)$ are parameterized by a bouquet of rational normal curves in $\mathbb{P}^{n}$ , and that the prime spectrum of $R(n,a)$ is homeomorphic to the Poisson spectrum of its semiclassical limit. Moreover, we explicitly describe $\operatorname{Spec}R(n,a)$ as a union of commutative strata.