A NEW FAMILY OF POISSON ALGEBRAS AND THEIR DEFORMATIONS

@article{Lecoutre2017ANF,
  title={A NEW FAMILY OF POISSON ALGEBRAS AND THEIR DEFORMATIONS},
  author={C{\'e}sar Lecoutre and Susan J. Sierra},
  journal={Nagoya Mathematical Journal},
  year={2017},
  volume={233},
  pages={32 - 86}
}
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… Expand
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