Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.18737 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914578612355072 |
|---|---|
| author | Franchi, Clara Mainardis, Mario McInroy, Justin Turner, Michael |
| author_facet | Franchi, Clara Mainardis, Mario McInroy, Justin Turner, Michael |
| contents | Axial algebras of Monster type are a class of commutative algebras generated by special idempotents called axes. Some motivating examples of these algebras are the Griess algebra and the Norton-Sakuma algebras, relating to the Monster simple group. A long standing open problem is to classify the 2-generated axial algebras of Monster type. A huge milestone was accomplished by Yabe leading, with additional cases completed by Franchi, Mainardis, and McInroy, to the classification in the symmetric case.
In this paper, we complete the classification. To do so, we split the proof into multiple cases: dealing with certain parameters, subalgebras, axets, and axial dimensions. Furthermore, we provide a basis, multiplication and information of the algebras in the classification; consolidating existing results on these algebras into one place. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18737 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Classification of the 2-generated Primitive Axial Algebras of Monster Type Franchi, Clara Mainardis, Mario McInroy, Justin Turner, Michael Rings and Algebras Group Theory 17A60, 17A99, 17C27, 20F29 Axial algebras of Monster type are a class of commutative algebras generated by special idempotents called axes. Some motivating examples of these algebras are the Griess algebra and the Norton-Sakuma algebras, relating to the Monster simple group. A long standing open problem is to classify the 2-generated axial algebras of Monster type. A huge milestone was accomplished by Yabe leading, with additional cases completed by Franchi, Mainardis, and McInroy, to the classification in the symmetric case. In this paper, we complete the classification. To do so, we split the proof into multiple cases: dealing with certain parameters, subalgebras, axets, and axial dimensions. Furthermore, we provide a basis, multiplication and information of the algebras in the classification; consolidating existing results on these algebras into one place. |
| title | The Classification of the 2-generated Primitive Axial Algebras of Monster Type |
| topic | Rings and Algebras Group Theory 17A60, 17A99, 17C27, 20F29 |
| url | https://arxiv.org/abs/2605.18737 |