(2B, 3A, 5A)-subalgebras of the Griess algebra with alternating Miyamoto group

2025/04/24 by Franchi, Clara, Mainardis, Mario
#17B69 #20C30 #20D08 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2504.17446

Abstract

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∈ \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.

Citations

• On the structure of axial algebras
• An expansion algorithm for constructing axial algebras
• Generalised dihedral subalgebras from the Monster
• 6-transposition property of τ-involutions of vertex operator algebras

Related

• Generalised dihedral subalgebras from the Monster
• Minimal 3-generated Majorana algebras
• Automorphism groups of axial algebras
• 3-dimensional Griess algebras and Miyamoto involutions
• Associative subalgebras of the Griess algebra and related topics