$2-generated axial algebras of Monster type $(2\beta, \beta)$$

2-generated axial algebras of Monster type $(2\beta, \beta)$

In this paper we prove that $2$-generated primitive axial algebras of Monster type $(2\beta, \beta)$ over a ring $R$ in which $2$ and $\beta$ are invertible can be generated as $R$-module by $8$ vectors. We then completely classify $2$-generated primitive axial algebras of Monster ty...

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Veröffentlicht in:	arXiv.org 2022-11
Hauptverfasser:	Franchi, Clara, Mainardis, Mario, Shpectorov, Sergey
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Mathematical analysis Vectors (mathematics)
Online-Zugang:	Volltext
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Zusammenfassung:	In this paper we prove that $2$-generated primitive axial algebras of Monster type $(2\beta, \beta)$ over a ring $R$ in which $2$ and $\beta$ are invertible can be generated as $R$-module by $8$ vectors. We then completely classify $2$-generated primitive axial algebras of Monster type $(2\beta, \beta)$ over any field of characteristic other than $2$.
ISSN:	2331-8422

Zusammenfassung:	In this paper we prove that \(2\)-generated primitive axial algebras of Monster type \((2\beta, \beta)\) over a ring \(R\) in which \(2\) and \(\beta\) are invertible can be generated as \(R\)-module by \(8\) vectors. We then completely classify \(2\)-generated primitive axial algebras of Monster type \((2\beta, \beta)\) over any field of characteristic other than \(2\).
ISSN:	2331-8422

2-generated axial algebras of Monster type \((2\beta, \beta)\)