In [15], Yabe gives an almost complete classification of primitive symmetric 2-generated axial algebras of Monster type, leaving open the case of algebras in characteristic 5 and axial dimension larger than 5. In this note, we complete the classification of these algebras, by constructing a new infinite-dimensional primitive 2-generated symmetric axial algebra Hˆ of Monster type [Formula presented] over a field of characteristic 5, and showing all the cases not falling into Yabe's classification are factors of Hˆ.
Classifying 2-generated symmetric axial algebras of Monster type
Mainardis M.
2022-01-01
Abstract
In [15], Yabe gives an almost complete classification of primitive symmetric 2-generated axial algebras of Monster type, leaving open the case of algebras in characteristic 5 and axial dimension larger than 5. In this note, we complete the classification of these algebras, by constructing a new infinite-dimensional primitive 2-generated symmetric axial algebra Hˆ of Monster type [Formula presented] over a field of characteristic 5, and showing all the cases not falling into Yabe's classification are factors of Hˆ.File in questo prodotto:
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