$(2B, 3A, 5A)$-subalgebras of the Griess algebra with alternating Miyamoto group
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913806734589952 |
|---|---|
| author | Franchi, Clara Mainardis, Mario |
| author_facet | Franchi, Clara Mainardis, Mario |
| contents | We use Majorana representations to study the subalgebras of the Griess algebra that have shape $(2B,3A,5A)$ and whose associated Miyamoto groups are isomorphic to $A_n$. We prove that these subalgebras exist only if $n\in \{5,6,8\}$. The case $n=5$ was already treated by Ivanov, Seress, McInroy, and Shpectorov. In case $n=6$ we prove that these algebras are all isomorphic and provide their precise description. In case $n=8$ we prove that these algebras do not arise from standard Majorana representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $(2B, 3A, 5A)$-subalgebras of the Griess algebra with alternating Miyamoto group Franchi, Clara Mainardis, Mario Group Theory Rings and Algebras 20D08, 20C30, 17B69 We use Majorana representations to study the subalgebras of the Griess algebra that have shape $(2B,3A,5A)$ and whose associated Miyamoto groups are isomorphic to $A_n$. We prove that these subalgebras exist only if $n\in \{5,6,8\}$. The case $n=5$ was already treated by Ivanov, Seress, McInroy, and Shpectorov. In case $n=6$ we prove that these algebras are all isomorphic and provide their precise description. In case $n=8$ we prove that these algebras do not arise from standard Majorana representations. |
| title | $(2B, 3A, 5A)$-subalgebras of the Griess algebra with alternating Miyamoto group |
| topic | Group Theory Rings and Algebras 20D08, 20C30, 17B69 |
| url | https://arxiv.org/abs/2504.17446 |