TY - JOUR
T1 - An infinite-dimensional 2-generated primitive axial algebra of Monster type
AU - Franchi, Clara
AU - Mainardis, M.
AU - Shpectorov, S.
PY - 2021
Y1 - 2021
N2 - 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 \r\nof characteristic other than 2 and 3. We further determine its group of automorphisms and describe some of its relevant features.
AB - 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 \r\nof characteristic other than 2 and 3. We further determine its group of automorphisms and describe some of its relevant features.
KW - Axial algebras
KW - Baric algebras
KW - Finite simple groups
KW - Jordan algebras
KW - Axial algebras
KW - Baric algebras
KW - Finite simple groups
KW - Jordan algebras
UR - https://publicatt.unicatt.it/handle/10807/184546
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85115302650&origin=inward
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85115302650&origin=inward
U2 - 10.1007/s10231-021-01157-8
DO - 10.1007/s10231-021-01157-8
M3 - Article
SN - 0373-3114
SP - N/A-N/A
JO - Annali di Matematica Pura ed Applicata
JF - Annali di Matematica Pura ed Applicata
IS - N/A
ER -