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 (,) over a field of characteristic other than 2, has dimension at most 8 if ∉{2,4} if α∉{2β,4β}. In this note, we show that Rehren’s bound does not hold in the case α=4β by providing an example (essentially the unique one) of an infinite-dimensional 2-generated primitive axial algebra of Monster type (2,1/2) over an arbitrary field
of characteristic other than 2 and 3. We further determine its group of automorphisms and describe some of its relevant features.
Original language | English |
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Pages (from-to) | N/A-N/A |
Number of pages | 15 |
Journal | Annali di Matematica Pura ed Applicata |
DOIs | |
Publication status | Published - 2021 |
Keywords
- Axial algebras
- Baric algebras
- Finite simple groups
- Jordan algebras