About

This website is dedicated to four-dimensional Artin–Schelter regular algebras. It is concerned with the quadratic (Koszul) case: algebras on four generators with quadratic relations — the noncommutative analogues of \(\mathbb{P}^3\). The non-quadratic cases are outside its present scope.

The families and their invariants follow arXiv:2511.08390 .

All of the family data — generators, relations, invariants and references — is also available as a single machine-readable file: data.yaml, assembled from the per-family sources in the repository.

The website is maintained by Pieter Belmans.

The source code lives at github.com/pbelmans/4d-as . Comments, corrections, and suggestions are welcome there: please open an issue, or send me an email.

How to cite

If you use biblatex:

@online{4d-as,
  author = {Belmans, Pieter},
  title  = {4d-AS-regular --- the classification of 4-dimensional Artin--Schelter regular algebras},
  url    = {https://4d-as.ncag.info},
  year   = {2026},
}

If you still use bibtex:

@misc{4d-as,
  author       = {Belmans, Pieter},
  title        = {4d-AS-regular --- the classification of 4-dimensional Artin--Schelter regular algebras},
  howpublished = {\url{https://4d-as.ncag.info}},
  year         = {2026},
}

Acknowledgements

I would like to thank Colin Ingalls. All remaining mistakes are my own.

This website is part of the CatsiNCAGe project. The author was supported by the Dutch Research Council (NWO) as part of the grant doi:10.61686/RZKLF82806.