2017/04/30 by Tom De Medts, Michiel Van Couwenberghe
Mathematics · #Algebra over a field #Algebraic structures and combinatorial models #Automorphism #Automorphism group #Connection (principal bundle) #Finite Group Theory Research #Group (periodic table) #Rings, Modules, and Algebras #math.GR #math.RA #msc:17A99 #msc:20B25 #msc:20C05 #msc:20F29
paper · pdf · doi:10.1007/s10468-018-9844-y
openalex created_date 2017/05/05 · arxiv created 2018/01/25 · openalex publication_date 2018/12/19 · arxiv updated 2019/05/07 · openalex updated_date 2026/08/05
We introduce axial representations and modules over axial algebras as new tools to study axial algebras. All known interesting examples of axial algebras fall into this setting, in particular the Griess algebra whose automorphism group is the Monster group. Our results become especially interesting for Matsuo algebras. We vitalize the connection between Matsuo algebras and 3-transposition groups by relating modules over Matsuo algebras with representations of 3-transposition groups. As a by-product, we define, given a Fischer space, a group that can fulfill the role of a universal 3-transposition group.