Recently Yabe gived 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 H of Monster type (2, 1/2) over a field of characteristic 5, and showing all the cases not falling into Yabe's classification are factors of H.
Franchi, C., Mainardis, M., Classifying 2-generated symmetric axial algebras of Monster type, <<JOURNAL OF ALGEBRA>>, 2022; 2022 (596): 200-218. [doi:10.1016/j.jalgebra.2022.01.004] [http://hdl.handle.net/10807/194060]
Classifying 2-generated symmetric axial algebras of Monster type
Franchi, Clara;
2022
Abstract
Recently Yabe gived 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 H of Monster type (2, 1/2) over a field of characteristic 5, and showing all the cases not falling into Yabe's classification are factors of H.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.