Automorphism-invariant Integral Forms in Griess Algebras.

[摘要] Motivated by the existence of group-invariant integral forms in various vertex operator algebras, we classify maximal automorphism-invariant integral forms in some small-dimensional Griess algebras, which are certain finite-dimensional commutative, nonassociative algebras arising in the theory of vertex operator algebras. An integral form of a rational algebra is the integer span of a basis of the algebra that is closed under the algebra product. The main method is the development of ;;integral form detector functions;; and an investigation of their properties. Each of the small Griess algebras we analyzed - the eight Norton-Sakuma algebras and three others - have unique maximal automorphism-invariant integral forms. This provides a canonically defined lattice and subring inside these algebras.

[发布机构] University of Michigan

[效力级别] integral forms

[关键词] nonassociative algebras;integral forms;lattices;Mathematics;Science;Mathematics