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

Clara Franchi; Mario Mainardis; Sergey Shpectorov

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

Rings and Algebras 2022-11-21 v3 Group Theory

Authors: Clara Franchi , Mario Mainardis , Sergey Shpectorov

Abstract

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 $2$ .

Keywords

axial algebras monster type 2-generated primitive algebras ring field of characteristic not 2 classification

Cite

@article{arxiv.2101.10379,
  title  = {2-generated axial algebras of Monster type $(2\beta, \beta)$},
  author = {Clara Franchi and Mario Mainardis and Sergey Shpectorov},
  journal= {arXiv preprint arXiv:2101.10379},
  year   = {2022}
}

Comments

31 pages. We added the discussion whether a symmetric 2-generated primitive axial algebra of Monster type $(2\beta, \beta)$ can also be non-symmetric with respect to a different pair of generating axes. This is possible only in the case of the algebra $3C(2/3)$. We also corrected a mistake in Theorem 5.7

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

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