Launching the website

This site collects what is known about quadratic four-dimensional Artin–Schelter regular algebras, giving the noncommutative analogues of \(\mathbb{P}^3\).

There are by now many such families, scattered across the literature: the elliptic Sklyanin algebra and its cocycle twists, graded (skew) Clifford algebras, the quadric-and-line algebras of Vancliff, the quantizations of Poisson structures coming from Pym’s work, the additive family of Lecoutre–Sierra, and a long list of iterated Ore extensions. The recent classification effort of arXiv:2511.08390 served as the starting point for this website.

Everything is generated from small data files. Corrections and additions are very welcome — please open an issue on the repository.

For now, this is still a draft, and I will not announce its existence publicly just yet. If you have found this website already, congratulations! It might look different soon.