Classifying 2-generated symmetric axial algebras of Monster type

Clara Franchi, Mario Mainardis

Research output: Contribution to journalArticlepeer-review


Recently Yabe gived an almost complete classification of primitive symmetric 2-generated axial algebras of Monster type, leaving open the case of algebras in characteristic 5 and axial dimension larger than 5. In this note, we complete the classification of these algebras, by constructing a new infinite-dimensional primitive 2-generated symmetric axial algebra H of Monster type (2, 1/2) over a field of characteristic 5, and showing all the cases not falling into Yabe's classification are factors of H.
Original languageEnglish
Pages (from-to)200-218
Number of pages19
JournalJournal of Algebra
Publication statusPublished - 2022


  • Axial algebras
  • Finite simple groups
  • Jordan algebras
  • Monster group


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