Abstract:We discuss some examples of nonassociative algebras which occur in VOA (vertex operator algebra) theory and finite group theory. Methods of VOA theory and finite group theory provide a lot of nonassociative algebras to study. Ideas from nonassociative algebra theory could be useful to group theorists and VOA theorists.
Keywords: nonassociative algebra, nonassociative commutative algebra, groups of Lie type, sporadic groups, vertex operator algebras, lattice type vertex operator algebras, axioms,
(B,N)
-pair, monster,
2A
-involutions, Jordan algebra, pairwise orthogonal idempotents,
E_8
,
E_6
, polynomial identity
AMS Subject Classification: 20D06 20D08 17A01 17B69