Enumerating 3-generated axial algebras of Monster type

Justin McInroy*, Sergey Shpectorov*, Sanhan Khasraw*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)


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.
Original languageEnglish
Article number106816
JournalJournal of Pure and Applied Algebra
Issue number2
Early online date17 Jun 2021
Publication statusPublished - 1 Feb 2022

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© 2021 Elsevier B.V.


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