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

Clara Franchi, Mario Mainardis*, Sergey Shpectorov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
57 Downloads (Pure)

Abstract

Rehren proved in Axial algebras. Ph.D. thesis, University of Birmingham (2015), Trans Am Math Soc 369:6953–6986 (2017) that a primitive 2-generated axial algebra of Monster type (α, β) , over a field of characteristic other than 2, has dimension at most 8 if α∉ { 2 β, 4 β}. In this note, we show that Rehren’s bound does not hold in the case α= 4 β by providing an example (essentially the unique one) of an infinite-dimensional 2-generated primitive axial algebra of Monster type (2,12) over an arbitrary field F of characteristic other than 2 and 3. We further determine its group of automorphisms and describe some of its relevant features.

Original languageEnglish
Pages (from-to)1279-1293
Number of pages15
JournalAnnali di Matematica Pura ed Applicata
Volume201
Early online date22 Sept 2021
DOIs
Publication statusPublished - Jun 2022

Bibliographical note

Funding Information:
Open access funding provided by Università degli Studi di Udine within the CRUI-CARE Agreement. This paper was partially supported by PRID MARFAP, Dipartimento di Matematica Informatica e Fisica - Università di Udine, and PRIN 2017–2020 “Teoria dei gruppi e applicazioni.”

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

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