Axial algebras of Jordan and Monster type

Justin McInroy, Sergey Shpectorov

Research output: Working paper/PreprintPreprint


Axial algebras are a class of non-associative commutative algebras whose properties are defined in terms of a fusion law. When this fusion law is graded, the algebra has a naturally associated group of automorphisms and thus axial algebras are inherently related to group theory. Examples include most Jordan algebras and the Griess algebra for the Monster sporadic simple group. In this survey, we introduce axial algebras, discuss their structural properties and then concentrate on two specific classes: algebras of Jordan and Monster type, which are rich in examples related to simple groups.
Original languageEnglish
Number of pages40
Publication statusPublished - 16 Sept 2022

Bibliographical note

39 pages


  • math.RA
  • math.GR
  • 17-02, 20-02, 17A36, 17A60, 17A99, 17C27, 17D99, 20B25, 20F29


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