Extended Griess algebras and Matsuo-Norton trace formulae
Hiroshi Yamauchi
TL;DR
This paper extends the Griess algebra to a superalgebra setting, deriving trace formulae that connect algebraic structures with group elements, and applies these to relate group elements with subalgebras in the Baby-monster VOA.
Contribution
It introduces the Z_2-extended Griess algebra for vertex operator superalgebras and derives new trace formulae based on conformal design structures.
Findings
Derived Matsuo-Norton trace formulae for extended Griess algebra
Reformulated correspondence between Baby-monster group elements and subalgebras
Established connections between algebraic structures and group theory
Abstract
We introduce the Z_2-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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons