Extended Griess algebras and Matsuo-Norton trace formulae

2012/06/15 by Hiroshi Yamauchi, Yamauchi, Hiroshi
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.1206.3380

33 pages

arxiv created 2012/06/15 · openalex publication_date 2012/06/15 · arxiv updated 2012/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the Z₂-extended Griess algebra of a vertex operator superalgebra with an involution and derive the Matsuo-Norton trace formulae for the extended Griess algebra based on conformal design structure. We illustrate an application of our formulae by reformulating the one-to-one correspondence between 2A-elements of the Baby-monster simple group and N=1 c=7/10 Virasoro subalgebras inside the Baby-monster vertex operator superalgebra.

Related

• Associative subalgebras of the Griess algebra and related topics
• Vertex operator algebras, extended E₈ diagram, and McKay's observation on the Monster simple group
• Vertex Operator Superalgebras and Odd Trace Functions
• Generalised dihedral subalgebras from the Monster
• 2A-orbifold construction and the baby-monster vertex operator superalgebra