3-dimensional Griess algebras and Miyamoto involutions
Ching Hung Lam, Hiroshi Yamauchi
TL;DR
This paper studies VOAs generated by 3-dimensional Griess algebras, showing they are uniquely characterized by these algebras and analyzing the groups generated by Miyamoto involutions.
Contribution
It introduces a classification of VOAs based on 3-dimensional Griess algebras and determines the Miyamoto involution groups associated with them.
Findings
VOAs are uniquely determined by their 3-dimensional Griess algebras
Characterization of groups generated by Miyamoto involutions
Explicit structure results for these VOAs
Abstract
We consider a series of VOAs generated by 3-dimensional Griess algebras. We will show that these VOAs can be characterized by their 3-dimensional Griess algebras and their structures are uniquely determined. As an application, we will determine the groups generated by the Miyamoto involutions associated to Virasoro vectors of our VOAs.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons