A NEW FAMILY OF POISSON ALGEBRAS AND THEIR DEFORMATIONS
A NEW FAMILY OF POISSON ALGEBRAS AND THEIR DEFORMATIONS
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 $n=3$ . …