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

Clara Franchi, Mario Mainardis, Sergey Shpectorov

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
1 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
JournalAnnali di Matematica Pura ed Applicata
Early online date22 Sep 2021
DOIs
Publication statusE-pub ahead of print - 22 Sep 2021

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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