On the center of 3-dimensional and 4-dimensional Sklyanin algebras

In this article, a new proof is given of the description of the center of quadratic Sklyanin algebras of global dimension three and four and the center of cubic Sklyanin algebras of global dimension three. The representation theory of the Heisenberg groups $H_2$, $H_3$ and $H_4$ will play an important role. In addition a new proof is given of Van den Bergh’s result regarding noncommutative quadrics.