## Abstract

An axial algebra is a commutative non-associative algebra generated by axes, that is, primitive, semisimple idempotents whose eigenvectors multiply according to a certain fusion law. The Griess algebra, whose automorphism group is the Monster, is an example of an axial algebra. We say an axial algebra is of Monster type if it has the same fusion law as the Griess algebra.

The 2-generated axial algebras of Monster type, called Norton-Sakuma algebras, have been fully classified and are one of nine isomorphism types. In this paper, we enumerate and construct the 3-generated axial algebras of Monster type which do not contain a 5A, or 6A subalgebra.

The 2-generated axial algebras of Monster type, called Norton-Sakuma algebras, have been fully classified and are one of nine isomorphism types. In this paper, we enumerate and construct the 3-generated axial algebras of Monster type which do not contain a 5A, or 6A subalgebra.

Original language | English |
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Article number | 106816 |

Journal | Journal of Pure and Applied Algebra |

Volume | 226 |

Issue number | 2 |

Early online date | 17 Jun 2021 |

DOIs | |

Publication status | Published - 1 Feb 2022 |

### Bibliographical note

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