## Abstract

Rehren proved in Axial algebras. Ph.D. thesis, University of Birmingham (2015), Trans Am Math Soc 369:6953–6986 (2017) that a primitive 2-generated axial algebra of Monster type (α, β) , over a field of characteristic other than 2, has dimension at most 8 if α∉ { 2 β, 4 β}. In this note, we show that Rehren’s bound does not hold in the case α= 4 β by providing an example (essentially the unique one) of an infinite-dimensional 2-generated primitive axial algebra of Monster type (2,12) over an arbitrary field F of characteristic other than 2 and 3. We further determine its group of automorphisms and describe some of its relevant features.

Original language | English |
---|---|

Journal | Annali di Matematica Pura ed Applicata |

Early online date | 22 Sep 2021 |

DOIs | |

Publication status | E-pub ahead of print - 22 Sep 2021 |

### Bibliographical note

Funding Information:Open access funding provided by Università degli Studi di Udine within the CRUI-CARE Agreement. This paper was partially supported by PRID MARFAP, Dipartimento di Matematica Informatica e Fisica - Università di Udine, and PRIN 2017–2020 “Teoria dei gruppi e applicazioni.”

## Keywords

- Axial algebras
- Baric algebras
- Finite simple groups
- Jordan algebras
- Monster group

## ASJC Scopus subject areas

- Applied Mathematics