English

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

Rings and Algebras 2020-07-14 v2

Abstract

Rehren proved that a primitive 2-generated axial algebra of Monster type (α,β)(\alpha,\beta) has dimension at most eight if α{2β,4β}\alpha\notin\{2\beta,4\beta\}. In this note we construct an infinite-dimensional 2-generated primitive axial algebra of Monster type (2,12)(2,\frac{1}{2}) over an arbitrary field FF with char(F)2,3char(F)\neq 2,3. This shows that the second special case, α=4β\alpha=4\beta, is a true exception to Rehren's bound.

Cite

@article{arxiv.2007.02430,
  title  = {An infinite-dimensional 2-generated primitive axial algebra of Monster type},
  author = {Clara Franchi and Mario Mainardis and Sergey Shpectorov},
  journal= {arXiv preprint arXiv:2007.02430},
  year   = {2020}
}
R2 v1 2026-06-23T16:52:07.714Z