# An infinite-dimensional 2-generated primitive axial algebra of Monster type

Research output: Contribution to journal › Article

## Authors

## Colleges, School and Institutes

## Abstract

Rehren proved that a primitive 2-generated axial algebra of Monster type $(\alpha,\beta)$ has dimension at most eight if $\alpha\notin\{2\beta,4\beta\}$. In this note we construct an infinite-dimensional 2-generated primitive axial algebra of Monster type $(2,\frac{1}{2})$ over an arbitrary field $F$ with $char(F)\neq 2,3$. This shows that the second special case, $\alpha=4\beta$, is a true exception to Rehren's bound.

## Details

Original language | Undefined/Unknown |
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Journal | Proceedings of the American Mathematical Society |

Publication status | Published - 5 Jul 2020 |

## Keywords

- math.RA, 17A99 (Primary) 17C27, 20F29 (Secondary)